"The baby is playing inside of the house"
Translation:Mtoto anacheza ndani ya nyumba
Yeah - nyumbani indicates a location associated with the house (to/at/in/on/from). Ndani ya nyumba more specifically indicates the inside of the house (into/inside/out of). You can also indicate this with nyumbani if you use class 18 concords ... but for that you'll need other words in the sentence (eg. nyumbani mwangu = into/inside/out of my house) because locative nouns themselves don't show which locative class they belong to ... so using ndani ya is much simpler if you really want to indicate the interior location. If you just say mtoto anacheza nyumbani that would mean the baby/child is playing at the house / at home ... and that could mean in the garden in some contexts ... so I think that's why ndani ya is used here - to stress the "inside".