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.
What about Peter came to mine? I know it's a bit of an assumption but...
Maybe due to my advanced age, but using 'home' in place of 'house', as in this sentence sounds faintly comic. I calls to mind real estate agents' sales blather. They always talk about selling 'homes' which is not actually possible. Only houses can be bought or sold. A buyer might make a house their home, or not. In my dialect this sentence would suggest that I don't live in a house, but rather some kind of home, like a home for the aged, a home for the disabled, etc. I have noticed that this genteelism has become more normal in America, though. So maybe I am just behind the times.