I'm curious as to why, "The women are mothers," is not also a valid answer.
In my opinion, it is invalid because Ābri and muñī would be in different cases (nominative and accusative respectively).
Ābri muñi issi. The women are mothers.
Does this sentence carry any distinction about whether the people being referred to are all mothers and women simultaneously or they are a group where some of them are mothers and some are women
I don't think it does any more than the English sentence. In other words, it can probably be interpreted both ways. But you would have to ask David Peterson himself. I think most readers would interpret it in the former sense though. You could rephrase the sentence to more clearly communicate one meaning or the other.