What happens if my current INT is 1025 and I move out of my house and then into a nicer one? Will I lose the INT over 1000 before I can move into the nicer one?

As far as I recall you will retain the higher INT so long as you don't gain Intelligence whilst not in the new house.

If that doesn't prove to be the case however you can get in touch with me and I'll restore any missing Intelligence.