It's one thing to not get something you never had...but to have something of yours taken away, is generally very difficult.
It's used in sales tactics; giving you the keys to a new car...letting you take it home even...makes it feel like it's yours, and you'll actually start to fight to get to keep it (oh, sorry, you'll need to pony up an extra $1,000...and you will because you don't want to lose "your" car).
For my purposes, I assign ownership to who has a financial claim on the item in question. If you just bought a $20,000 car with $0 down, then I consider that car to be the bank's. If it's a $20,000 car with $10,000 owed, then you and the bank are equal owners. Same with houses; more than once someone would ask about "our" house and I'd reply that it's actually the bank's.
I also get the fact that you wouldn't want to affect the children. You have to consider everything. Not just "Oh no, they'll be devastated if they have to leave their house/school/friends." But also "We can stay for an extra three years, be stressed the whole time which will affect them, eventually lose the house anyways and possibly get divorced." Kids can probably handle a move pretty easily, as long as the family's intact.