I think your measuring should be the law. If she does something that violates the law then take action. If Mr. X turns out to be abusive to the kids, take action. These things are hard on kids, there is no way to avoid that. Every new BF for her or GF for you will be stressful for the kids. All you can do is be as stable and strong for your kids as you can be. Is their mom going to do things that they get upset over? Absolutely. You probably will too at some point.
Focus on what you can control.
M(51), W(52),D(16) M-20, T-23 Bomb Drop - Dec.23, 2017 Ring and Piecing since March 2018