Firstly, you left your kids with her? She sounds really unfit when she is drunk. That is scary to me. What kind of protection do your kids have when she is like that?
It sounds like the two of you each have issues to work out before being with anyone else. Your primary relationship with yourself is in need of work it looks like. Then your relationship with her. Starting there seems like your best chance at later success.
Usually someone that "doesn't feel like a man" or feels jealous even though they are doing whatever they want has some self worth and self esteem issues. Being threatened like that when you are doing whatever you want is just hypocritical. Looking at what it is that threatens you and creates fear for you when she sleeps with other men might be a good place to start. What do you feel when you do this. Is your love different after? She is likely feeling similarly. Empathize and attempt to walk in her shoes to see what she might be feeling and to see if you can change how you feel about it.
Personally it seems to me that you are done in this relationship and need to concentrate on yourselves now. Please don't bring other people into your craziness and think it will work out. Maybe being open and just doing your own thing would be better. Sharing a lover in your state would be destructive and unhealthy to that unsuspecting person and that isn't fair. No one deserves that and the two of you seem unfit to be able to handle what comes up in your own relationship let alone one with another person added. Its like having a kid to solve marital issues. Doesn't work.
This isn't likely what you want to hear, but its my two cents based on what you have said. Good luck.
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