OP - I believe your theory is possible. I had the same thoughts. But I haven't been able to find a single source that states Jill babysat Joe's kids. I found that Jill worked on Joe's campaign 1-2 years prior to his wife's accident. Nothing about babysitting.

Also, maybe Jill knew about Joe's pedo predilections and drive her and the kids into traffic when she found out about the affair. That's why Joe lied about the truck driver for all of those years...to cover his guilt.