|My question is this: you are all talking about a new trial. Wouldn't that be considered double jeopardy? Or would they prosecute her for the other kids?
Double jeopardy attaches when someone has been through a trial, and has been found not guilty.
As Allissa said, if one is found guilty, and that conviction is overturned on appeal (appeals generally don't assess the guilt or innocence of a person, with rare exception regarding new evidence), it is back to the beginning. The DA's office will have to sit down and reassess the likelyhood of a conviction and/or a plea, and go from there.
The DA's office has an opportunity to appeal the overturning of the conviction, and I think they will challenge it. But I also think it will stick, so like I said, it's back at the beginning.
As for them trying her on the other two children, I think that's a possibility. It's a fresh, new case without appellate issues, and they have a good idea of what the defense is now. They are also intimately familiar with all aspects of both cases, and I can easily her getting charged with the two murders, and then secondarily charged with the original three once appeals run out.