I get it, we bought a doer upper with a teenager, toddler and two housecats. We are obviously insane.
Anyway, we have so far has the kids bedrooms stripped and plastered, new carpets, knocked down a wall, bricked up 2 doors, had patio doors installed, kitchen out (and haven't had a proper kitchen in 3 months!) walls plastered, painted, then a new kitchen in oh and a full re wire and we still have to do the floor in there, as well as;
every other wall to be stripped and plastered in the house
every other room to be carpeted/wood floored
new bathroom eventually
tackle the garden
so far no cats have escaped, and the teen and toddler have been at school and nursery.
The cats have felt a bit inconvenienced I think, but they haven't suffered particularly. I just made sure everyone was aware that they were not allowed out under any circumstances and so far so good.
it has been stressful, and living in clutter is driving me slowly insane BUT my advise would be, do not do it all at once if you can avoid it.
Make sure you have a room at least, that remains untouched, with no furniture in it that doesn't belong there, so you have somewhere to relax that doesn't feel like a building site.
I am going to be very cliché here, and I have wanted to scream at everyone who has said this to me but "it will be worth it"
it may not seem like it now but you will be glad you've done it when its over.