I'm so sorry you are having to go through all this. It's a horrible thing to live through.
While I know nothing about marriage and can offer no advice there, I do have experience in the child's side. My parents were together since they were 15, married at 19. I came along two years later. There were apparently signs of problems with my dad and other women even then, although my mom doesn't know when the cheating actually began. She didn't leave him then because she was too proud to admit failure.
I always knew there was something wrong with my dad, and it didn't take me long to figure out that he was cheating once I knew what that meant. Kids aren't dumb. I hated my father, but also resented my mother for not leaving him. I begged her for years.
She finally let him get a divorce after 24 years of marriage and four kids. She let him design the terms of the divorce and they didn't get a lawyer. She has had to live very simply while he has gone on to make (and lose) lots of money.
My dad is on his 7th marriage and miserable. My siblings and I only have contact with him out of a weird sense of duty. He has lost everything, since some of his ex's were smart enough to get good lawyers.
So while no one can tell you what to do, in my experience the kids will be happier getting out from under all of it. Try to stay cordial. Fight for your rights to the kids. They need love and lots of it. Give them all the stability you can. Kids are pretty resilient when they see that both parents are okay and making new lives. It's not ideal, but I think it can be really, really good.
Good luck! It's gonna suck for awhile but you'll get through it.
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