"You remembered my children."
Translation:Usted recordó a mis hijos.
You're right.Both are obviously possible.This app has major flaws for all its good points.
When the direct object of a verb are people or pets, there is an 'a' before it. It is called the personal 'a'.
tú recordaste a mis hijos is also perfectly fine, since 'You,' could be both formal and informal!Not record-'iste' as it is 'aste.'
The problem is mis niños. See, niños = children as non-adult people, not necessarily descendants, so saying mis niños sounds like you own some children.