Your thoughts say a lot about what you already know to be the appropriate action. I have shared with another that relationships so soon after one falls apart are more like a drug to lessen the pain of the loss.
If you really want to know if you are okay when she is not around, you may want to think about taking a break from it for a period of time. Say a month or more. if you truely are okay without her around this will help you know for sure.
Aside from that you outline more red flags than anyone that has gone through what you have and learned what you have should even still be considering. She sounds like she is jumping into relationships before she has done some major healing of her own.
IMO you have enough on your plate to focus on for yourself and your kids to be trying to figure this out. Remember that what you decide to do does not just affect you and her........ Ponder on that my friend.......
Be well this evening.
Me 46 Former W 46 D19 D7 BD Feb 2016 WAW moves out 4/16/16 D final 6/1/2017
It's time for me to start changin' the way I look at the world......and at myself. ~James Howlett aka Wolverine