Well, they shouldn't be. Changing cultures and attitudes is the single most interesting thing about AH!
Well yes but what I meant was that there were no social trends which were tending towards the two states growing to love one another, so what is needed is a totally unexpected event which changes attitudes and breaks the trends - and this naturally becomes unpredictable and the realm of TLs written for the long term rather than speculation on near history. That is to say, I can't see a single event in the history of the two states which could have gone one way or the other which could have brought about this situation - it would need something unexpected.
Is there a way to engender cooperation between the two states early on in the personal union? George I disliked Great Britain and became its King somewhat begrudgingly. Could a different attitude from him have changed the perspective of his two bodies of countrymen - or at least, begun to change that perspective?
An early death of the Old Pretender, leaving George as the undisputed heir, might make him more universally popular in Britain.
There might be more. But I find it more enjoyable to explore possibilities.
Really what it needs is something to happen which puts Hanover's existence in threat, and which necessitates them seeking British help - it goes to say this event would have to be in the British interest. Of course the reverse could work too but I can't see many situations where the UK needs to rely on Hanover to see it through a dark period. Maybe, given the Prussian unification of Germany, this would provide the required threat to persuade the Hanoverians to bite the bullet and go down on their knees in front of Parliament - it's possible, I'm not sure how averse the Hanoverians were to annexation. But in order for this to work, you need to alter the line of succession - and not the law of succession. As said before, the Hanoverians didn't really like being in Personal Union with the UK because they didn't see themselves getting anything out of it, so they aren't going to change Salic Law before this troublesome event happens. The alternative that I can see is you play with the Napoleonic Wars and have Napoleon play around with Germany in a different way, threatening to eliminate the Electorate and divide it up between...some other local power that the Hanoverians don't want to be a part of. Maybe threaten a partition between Prussia and Westphalia, or something. If the British are then able to stop this plan (probably by beating Napoleon at Waterloo, as I can't see a British invasion of Germany being strategically sensible) and - probably in spite rather than because of their planning - be seen as the country which kept Hanover whole then you could see the start of this situation falling together - but it's hard to say. Or maybe you could have Prussia and Austria both be very heavy-handed with their Zollvereins, leading Hanover to pull away from joining Prussia's, and rely on the British to survive Prussian anti-competitive trade regulations. If, for instance, some other northern German states such as Hamburg, Brunswick, Oldenburg, etc were to ask Hanover to form their own Zollverein it's doubtful the Hanoverians could make it work without British backing. But these situations are all prone to not working out the way you want.
This is what I was talking about when I said you'd need to invent a scenario, though, really. There are too many ways that things like this could improve the situation but not really get you where you want to go. If you were to write a TL and make up your own event to create this situation it would be far easier to control and to actually achieve what you want to achieve. The previous situations, for example, aren't great because as soon as Napoleon is gone Hanover doesn't need British backing and will soon forget their plight, and there's no reason for Prussia to act roughly with Hanover before their wars to unite Germany. Still, hopefully it gave you some ideas.