It's the possessive (i.e. words like my, your, his) that must be used when the person doing the possessing is also the subject of the sentence. hamaara means "our," yes. But one can't say, "ham hamāre ghar meṅ..." One must say, "ham apne ghar meṅ...". "apnā" could roughly be translated as "one's own".
It's the oblique case. अपना changes to अपने, the oblique form of घर is also घर (because it's male singular unmarked), so one does not see the change there.
In this sentence is a postposition (में) which demands that the oblique case be used.
ok. it was my typo in another word... can't delete comment from mobile app