First – let’s put the focus right now where it belongs. There are 4 children who need to be loved and financially supported. It’s not about a competition with the other woman. In fact, you have more in common with her than with the guy you are both foolish enough to want. Both of you have been disappointed. Neither of you can trust the father of your children. Both of you may be left to raise these children on your own.
You and the other woman are actually related to each other through the kids since they are all siblings. She has taken nothing from you, any more than you have taken something from her. Whoever the guy ends up with, you and she will be co-parenting all 4 children as the kids go back and forth between the homes. I think both of you women would do well to call a truce and to meet together regularly to figure out how you are going to raise the children. You two could become a better team than either of you can expect to get out of the guy. Further, you should both be seeing a lawyer so that you are sure what your rights are regarding financial child support and visitation rights in your state.
It’s unlikely that either of you will manage to make a stable marriage with the kids’ father. Focus on giving the children what they deserve for now. Once the dust has settled, I hope you will find a guy who deserves your love.
I wish you well.