Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...
First off, serial cheaters, are just that and the likelihood of change is horribly low. She also has mental health issues which makes her even less likely of being able to sustain healthy relationships in general.
She is not marriage/relationship material and you need to protect yourself and your children from her. She has no intention and may not even be capable of keeping her vows....which she hasn't even made yet.
Staying with a cheating boyfriend/girlfriend is a poor decision, marrying a serial cheater is much worse. You are all but guaranteed to have a disaster of a marriage.
I understand you have kids with her, which complicates things. Make sure your financial assets are protected.