In my opinion: your situation is part of the problem with our western civilization. Do crappy things that make us feel guilty, but are somehow culturally acceptable; then the "professionals" give us drugs to dull the effect of the pain we cause and to make us too blurred to make good choices. That is another topic... on to the one at hand...
In my opinion: it really is all quite simple. There is a clear path to feeling connected to yourself again. The path to feeling strong, happy, like you are a good mother and a good prospect for a poly relationship is there, but is a very difficult path at this point.
In my opinion: you need to get your priorities straight. Those kids are your first priority. If they are being affected then you have major shit to fix. They have a right to a mother who is strong, knows how to handle herself and is a good role model. You are not any of those things right now by the sounds of it.
Second priority is to deal with your guilt and fix what you have fucked up. You need to live with that guilt on your own as it is your problem and not your husbands. I totally agree with Quath's wife (you have a good woman there Quath!) It is your punishment to feel guilty and entirely unfair to put anything on to your husband. He should never know, firstly, for your sake, as he thinks you are a wonderful wife and mother in his heart and, secondly, for his sake in that he does not deserve the burden of your fuck ups. It is not okay to give him that burden. Take it from me, who has done it before, it does not make your guilt go away to let your partner know that you have been unfaithful! It makes it worse as you see their pain and it is ten times worse than your own!!!!.... please please consider that if nothing else I say!!!
Lastly is the unemotional stuff.... set your emotions aside, be rational and weigh it all out. Is he worth staying with? What are the things you loved about him? What did you find sexy about him? Is he a good man? Do you admire him and look up to him as a person? Would you be better off being really good friends that raise kids together separately? Or could you live in the same house be friends and raise kids? Could you ever be lovers again?
Dump the man friend you are seeing now immediately telling him that you no longer want to hurt his wife (who I assume doesn't know) by being in his life and suggest that he take a good long look at his own life. Also tell him that he may not see it now, but you are doing him a big favour by pulling yourself together and getting what you need out of your life. Be an example to him of what can be accomplished when you act out of love for others and yourself, not out of greed and self serving motives because YOU are not being fulfilled.
Then do it, decide that you are not going to see the man again, decide that you are going to go out and take on your life because you owe it to your self and others who love you to do so. Love the people in your life enough to realize that even though your actions from here on in will be difficult for them at the beginning they will benefit from your happiness, sense of well being, courage and ability to move towards a better life. It will inspire them to do the same if you do it with empathy, compassion and love. Be the person you think is worth loving.
I am so glad that you told your story because it is SO familiar to so many. It breaks my heart to hear people suffering by their own actions and the action of others. It's because you have told your story that you can move forward, that others can move forward and that I can give some of my hard earned wisdom on the topic....for that I am thankful. I feel for you, I really do, as I have been there and have talked long and hard about my own story, listened and strategised with others.
You aren't alone, many of us on here have struggled. You have a chance to show the world what you are made of and give your life all you've got. I really hope you do that and can stand proud. I do now and there is NOTHING like it
go do the right thing.