Kitchen's don't own their walls do they? The owner of the building owns the wall, so the first option is out.
The last two options are semantically equivalent but "his" is ambiguous. It might become evident in the context, for example:
Joe had a Little in his house who was stealing food. Finally, one
of our neighbors broke his kitchen wall open and got her.
I would just remove the ambiguity and go with:
Joe had a Little in his house who was stealing food. Finally, one
of our neighbors broke Joe's kitchen wall open and caught her.