Use of "घर में" places emphasis on Peter having come 'inside' your house and is somewhat uncommon.
Generally, the postposition that is equivalent to the preposition 'to' is 'को'. However, it is often omitted when talking about a destination (eg: मैं बैंगलोर जा रहा हूँ -I am going to Bangalore).
It's because 'मेरे घर' is in the 'oblique case' in this sentence. This is when a noun is the object of a postposition. This sentence does not have a postposition as such but 'को' (corresponding to the 'to' in the English sentence) is implicit which is why 'मेरे घर' is in the oblique case. The oblique form of मेरा is मेरे.