"His children were at my friend's house."
Translation:Seine Kinder waren bei meinem Freund zu Hause.
Your sentence could also mean that the children only stood before the house. It does not specify that they set foot in it.
Agreed! In fact, if someone says this in German I would assume that the children probably did not set foot in the house.
The English sentence here also doesn't specify that the children were inside the house. They could have been outside it, for example, in the backyard. They would still be "at the house".
Would any of you "indigenous" folk tell me, is this the most common way of saying "at someone's [my friend's] house?" And/or is, "in dem Haus meines Freundes" used as frequently or only in literary publications? Vielen Dank.
I think "bei meinem Freund zu Hause" would be best. "In dem Haus meines Freundes" is very emphasized, as in 'inside the house not on the house' in case you are repeating yourself to someone who didn't catch what you were saying.