Kim, I have to agree with Michelle here.
We both bred and trained what are considered "aggressive" breeds, because they excel in police work etc.

In this instance, the safety of the kids is highly jeopordized, I am sure Michelle remembers Conan a wonderful Rott import from Germany, he also had little tolerance for kids, and Rotts are usually wonderful with them. He was also placed (we are going back 15 years here guys), In a show home with no kids.

The behaviour you are describing is actually a fear type of aggression, I know it doesn't appear that way on the surface, but my guess would be that she got her butt whooped by a human or dog that appeared submissive. I.e. a person lying down, playing with her and all was well maybe a puppy nip set the human off who then yelled or hit or badly corrected the behaviour, or another dog that was on their back or in play mode that played too hard and hurt her.

Another thing to consider, if she is a mix of bully breeds, and you have no info on her past, it is very possible that some idiot used her in a bait situation, she now has a taste of dominance and safety in her mind so her fear creates the aggression issue with anything submissive, in other words she doesn't have the confidence to be dominant so agression is used.

Please be aware that this can escalate very quickly, and lets face it anything larger than a Pom (you all know what I mean) is a real threat to any child. My own dogs included if they were so inclined. The childrens safety is priorty here as you said. I would seriously consider helping her rehome this animal for her sake and for her human siblings sake.
Just my opinion.

Kym