I had to reread your question. Where I come from if you have children with a woman usually that means you are also her husband as well as the children’s father. No judgement just how I was raised and why your question confused me at first. Hell if you’ve had kids with her than you guys already know each other on a sexual level. Seems natural to continue that relationship even if she is with another man. I mean realistically you should be her husband anyway. That is my take anyway. Just don’t get yourself shot when her husband returns from overseas. Good luck as you maintain a relationship with your kids and their mother on whatever level that seems appropriate to the two of you.