She demands a divorce, he moves out next door but eat with family on Shabbos, now he sees there is no easy Sholom bayis fix , who has to move out if a get is given?
There is no simple answer to this question, and it is generally part of the divorce agreement.
The house generally belongs to both partners, the matter depends on the agreement reached by the parties, for instance that the wife stays in the house with the children in place of child support payments.
It is noteworthy that the Gemara rules (Kesubos 28), concerning a question of which partner has to move out of the neighborhood, that the ex-wife must move out, because moving is harder for men than for women. However, for a jointly owned house this rationale will not apply, and an agreement will have to be reached.
At the worst, the house can be sold, and nobody will get to stay there.