It's complicated and would take a lot of work. Our constitutional monarchy is bound up in lots of aspects of life - parliament, laws, armed forces etc. Whoever decided to dismantle it would have to amend all the different laws, rules, traditions to remove (and possibly replace) the role of the monarch with a different head of state, or something else (?)
It would be years of work - and probably considerable cost so the political party which goes for it needs to be sure there's enough public support for it otherwise it will be political suicide.
Also, for the PP who said would the Windsors decamp to Ottowa - very unlikely - their lives would probably get a million times easier - they'd just be able to retreat to the homes they already own - Balmoral, Sandringham, Highgrove etc. And just get on with enjoying all their private wealth.
They'd lose the Duchy incomes presumably but then again they wouldn't need to staff the palaces, or the Crown estate properties or run them in any form as they'd be all run by the government. Or sold off?
Andrew and Edward's families and the Queen's older cousins would need to find somewhere else to live. Everyone else has their own privately owned residences.
They'd probably all keep their titles too - unless the political party who goes for getting rid of the monarchy decides to take away all inherited titles and that is VERY unlikely considering how rich, politically influential and powerful a lot of the people with titles across the country are.
I think the far more likely scenario after the Queen dies is the British Royal family slim down the 'working members' return a lot of the big properties over to more public use (Charles apparently has suggested Buckingham Palace could become a public museum) and we'll end up with something much more modest like the constitutional monarchies of Belgium, Spain, Netherlands etc.
Charles is a bit of a spender though so I don't think his reign is going to be popular - I can see William achiveing the slimmed down version though.