The Falklands war saved Thatcher's rear-end big time. Prior to the war, the SDP-LP Alliance polled above 50%.
What if the Falklands War were avoided (Maggie never cuts back on the security in the islands) and the Alliance won an overwhelming victory?
I think you are overestimating the importance of the Falklands to be honest. There were signs that the Tories were improving prior to that. The Alliance's were polling well prior to then, but they only hit 50% in one poll. The improving economy would inevitably strengthen the Tory revival, and if things are looking bad in 1983, they can always wait until 1984 to call an election. You might see a few more Tory defections without such a sudden turnaround in the Tories fortunes thanks to the war, but I still think the best case scenario for the Alliance in such a situation would be a hung parliament where they beat Labour in the popular vote but are only around where they would ultimately end up in in the 2000s in terms of seats, and they have to prop up the Tories.
That said, I think there is a chance for the Alliance to win first time out, but I only see two scenarios where that could happen. One is to have an election take place when it was at its polling peak in 1981, which is difficult, given that the size of the Tory majority was probably large enough for them to have the next election at a time of their own choosing, even if they also suffered mass defections to the SDP. So you'd need a pre-1979 PoD, before the party was created, which gives Thatcher a majority large enough for her to pursue a monetarist agenda that generates a significant backlash, but small enough not to withstand a significant number of defections. So probably around 40. Then, you could have an election in 1981, which the Alliance would be likely to win, quite possibly with a majority.
Alternatively, you could have the Falklands War still happen, but Britain loses somehow. Maggie resigns, is most likely replaced by Whitelaw, and the resulting backlash and division does damage to the Tory brand that can't be repaired by an improving economy. Support for the Alliance revives, they win some more by elections, pick up support in the press, and emerge as the largest party in 1984, and go into coalition with the Tories, who they could then destroy at the next GE. That still feels slightly handwavy, but I think its plausible.
I imagine there'd still be a shift towards economic liberalization, but without the issues of Thatcher's personality they might settle a bit better.
Jenkins was the designated Prime Minister, so I assume it goes to him.
Could a successful Alliance have gotten the Wets to coalesce with them?
There would still be economic reforms, but they probably wouldn't go as far as Thatcher's. The Alliance took a lot of inspiration from Germany, they believed in a consensus based approach to industrial relations, so you'd probably see workers on company boards and things like that. A shift of emphasis in the way collective bargaining is done, rather than basically abolishing it in the way Thatcher did. They also didn't like the idea of constantly shifting the frontiers between public and private, so you wouldn't see as much privatisation as Thatcher pursued (though I wouldn't rule it out in the longer run), but neither would you see much nationalisation either.
Another important consequence would on constitutional matters, STV would be introduced (which would probably mean the alliance doesn't fight the next election on a joint platform) earlier devolution to Scotland, and they would probably at least push a referendum in Wales, which could actually have the effect of killing devolution there, as they would quite likely reject it, given the overwhelming margins against in in 1979, and I don't know that proposals for an assembly could survive two defeats in less than a decade.
With regards to the Tory 'wets' I think a lot would depend on the exact circumstances with the Conservative Party. But I think that the upturn in the global economy would probably see at least part of the alliance (if Jenkins was PM the SDP would probably take the lion share of the alliance vote if they contested separately) returned to government at the next GE. If the Tories don't elect a right wing leader after 1984, then they probably would at some point later after losing another election, in which circumstances, I could see many of the wets coming over. I could see some of those who lost their seats, and therefore have no jobs to worry about anymore, coming over straight after 1984, to be honest.
Ultimatelty, I think both the SDP and the Liberals will end up falling back to third place if PR is implemented. I can't see them being able to wipe out either the Tories or Labour altogether as parties of government if you have STV, and since they won't work with each other, as soon as the alliance loses an election, they are likely to be called upon to join a coalition. So, like the SPD, they'd have a lot of influence over governments, but that would come at the price of a persistent electoral decline.
If, on the other, hand FPTP stays, you'd probably see a party system which primarily pits the Alliance against Labour. The nature of the electoral system would probaly compel the Alliance to stay together though, and the Owenites would not take kindly to that. I once had an idea for a PM list that involved an Alliance-Conservative coalition in 1984, followed by the Tories losing all but a handful of their seats to the alliance at the next election, and after the Alliance votes to stay together indefinitely after that, David Owen leads a new breakaway party from the SDP which unites with some of the Tories who were too right wing for the SDP, but too left wing for the Tebbite Tory Party that was emerging- like John Major. Ultimately, you'd have a two and a half party system consisting of a Jenkinsite SDP, a Kinnockite Labour, and an odd party that is third way on economics, but also eurosceptic and populist playing a similar role to the Lib Dems.
An Alliance Government would most likely be short-lived, possibly only lasting a year at most
This was because the Liberals and SDP, although both broadly centrist, had several differences between them which, while easily hidden in Opposition, would be exposed in Government. Indeed, the only issue uniting the two was the need for Proportional Representation.
Not sure where you got that from. The leaders of both parties actually agreed on quite a bit- a mixed economy, devolution, industrial democracy, and pro-Europeanism, to name but a few. They arguably got along better than the opposing wings of Labour and the Tories during this time. I think a lot of your perception is based on the Owen years- but Owen was more right wing than the rest of the Gang of Four, and in the Jenkins era, relations were much more harmonious. What's more, some of the main divisions, like on the nuclear deterrent, could be butterflied away by a 1984 election victory, as that was caused by introduction of the Trident, which both the SDP and the Liberals were opposed too beforehand, but the SDP wanted to stick with once the money had spent, since their objection was mainly cost based.
I actually think the biggest divisions in an alliance government would not be between the two party leaderships, but between each of the leaders and the rest of their party. Steel would probably be faced with the objections of his party's radical wing, and Jenkins would have to deal with the Owenites.
Sure, Labour may have been in second pre-Falklands, but if we assume that the Alliance maintains its polling lead throughout 1982, 83 and 84, the Conservatives would still recover and move ahead of Labour due to the improving economic outlook. Also, it is important to factor in that the SDP's target electorate was Labour voters disenchanted by the Party's lurch to the far-left, so any SDP surge will come at Labour's expense.
Its true that the Gang of Three largely initially wanted to create a party that would essentially replace Labour- but in reality that wasn't ever workable because their appeal was primarily middle class. The result was that they did replace Labour in the south of England-where their vote was largely middle class, but also sparsely distributed. So they effectively siphoned off the section of Labour's support that was the least efficient in turning votes into seats, whilst making few inroads in working class constituencies. That was why the Alliance would find it so difficult to crack the Labour vote. It's also why you can end up with an absurd situation in 1983 where Labour have come third in the popular vote, but first in seats. They had a firewall of support in the north that will ensure they remain a major party.
To win first time round, the Alliance would need to take mainly from the Tories, because that was where practically all of their marginals were.
Now, unfortunately Electoral Calculus doesn't distinguish between the Liberals and the SDP, but if we assume for a moment that two-thirds of the Alliance's MPs are Liberals and the remaining third are from the SDP, then we would have 225 Liberals and 112 SDP MPs (granted, this is not the best way of determining the composition of the Alliance in this timeline, but its certainly the quickest rather than strolling through all the constituencies which the EC has as an Alliance gain).
I'm really not sure about that. Granted, the Liberals provided the bulk of the Alliance gains in 1983 and 1987- but this was because they were good at securing the nomination in the most marginal of seats. From what I've read, the seats were apportioned so that it would have been fairly even between the two parties if the Alliance had won more than 50 or 100 Seats. In fact, in the scenario you've outlined, the SDP would likely be more dominant, as they generally were selected to fight Labour seats, whilst the Liberals were more likely to fight Tory marginals, so which party collapses to give way for the Alliance is going to be important in determining which party of the two is larger.