I disagree, massively. If Hoche had succeeded in landing and then conquering Ireland - a big if, requiring a mixture of massive French luck, enthusiastic Irish support and spectacular British inertia - then Britain is toast, likely even finished as a great power.
You're exaggerating. But first things first, Hoche never meant to conquer Ireland. I'm not sure that was ever in the cards at all. I think the Directory only did so to keep Paris from revolting against their unpopular government. Now, with British defences in Ireland in 1796 far weaker than those in 1797, and with a much stronger Society for a United Ireland, you'll probably see a massive chunk of Ireland under the control of a "Hibernian Republic". But then, with loyalist guerrillas throughout Ireland against the French and a large number of British forces being brought into Ireland, they'll eventually be defeated, and hopefully Hoche will be able to use this popularity to overthrow the counterrevolutionary Directory. As well, it'll create a dream of a non-sectarian, secular Ireland, which will have deep effects on Irish nationalism.
A great deal of their food came from Ireland, they heavily relied on it's charcoal and timber (the reason that Ireland is still the least forested country in Europe), and leant heavily on it's manpower.
In regards to the food issue, if memory recalls, Britain was still self-sufficient at this point, and even IOTL, there were a bunch of major naval mutinies in Ireland that didn't severely affect their ability to fight in the war, so manpower isn't that great of an issue.
Additionally, there wasn't one great family in England that didn't have huge holdings there. Their economy would have taken a critical hit, which would have crippled their ability to fund the war for the Allies or even fund their own operations.
I don't doubt this. There'd be a massive gold run on the bank that would make Fishguard and its results look like a minor market correction, and Luddite riots would also begin many years earlier.
A successful operation would have encouraged the Directory to stand on the defence in Europe and pour everything they have into Ireland, which butterflies Bonaparte to a large degree.
Here, I must dispute the role that money played in French advances. In Italy, which was the main area where the Directory advanced, it was mostly extremely-successful reforms and Bonaparte's skill that allowed for such a massive advance, and he also did this fairly independent of the Directory - see the Roman and Parthenopean Republics, in which Napoleon took the Papal States and the Two Sicilies entirely independent of any Directory decision. So, I suspect you'd see massive advances in Italy and a march to Vienna regardless. The only thing is, this probably butterflies Egypt, so without the taking of Malta by Napoleon's fleet and the anger this will give to Tsar Paul, Suvurov won't be in Italy, so I suspect a weaker advance by the Coalition in Italy.
The British would have forced to make peace and beg the French to let them have Ireland back. Which the French seriously ought not to do
Again, a bit of an exaggeration. I suspect Pitt's government will fall, and a more accommodating government will then sign something like Amiens. However, I suspect this treaty may have a chance of holding, what with Britain mired in domestic troubles.