Translation:Mom is going to the store with a child.
The logic here is that if the verb follows "Мама с ребёнком", it assumes the form applicable to both of them, i.e. plural. If it follows just "Мама", it is natural to make it singular. This rule is not 100% strict though, and given the relative freedom of reordering sentences in Russian, I would only be able to tell you what sounds natural and what doesn't.
Still marked wrong as of 5 Feb. 2018.
This was the "answer" proffered by DL: "Mom with the child go to the store."
I thought I'd seen everything. I realize that native or near-native fluency in Russian was the primary consideration when choosing moderators for this course, but shouldn't DL demand some modicum of English literacy? How is anyone expected to complete an exercise when the required "answers" are so grammatically indefensible?
Yes, and it certainly sounds better than "Mom is going to the store with a child." (Who is with a child here, the mother or the store? Given the indefinite article, I suspect the latter.)
One comment though: I've noticed that Duo is quite strict about formal/informal dichotomy as far as parents are concerned: mum/mom=мама while mother=мать. The same goes for dad=папа while father=отец.