It is a more liberal meaning for the sentence, but the word aquela is not immediately before casa. So, the first answer is to follow the same word order here.
is 'dos' is plural because of the word 'filhos' (despite 'casa being singular)? so "Those are my son's houses" would be "Aquelas são as casas do meu filho"?
You say you wrote "my sons" house"; I'm sure you meant to write "my sons' house" instead but if you didn't then that's probably why Duolingo flagged a typo.
Because the Portuguese talks about more than one child. Your sentence translates "Aquela é a casa do meu filho."