If you were my wife it would have been over when you cheated, that is something I would neither do nor forgive, ever. If I did somehow forgive you and you contacted the person again, not matter how innocent, it would be over then and there. There are some deal breakers for me, and this is on the top of the list.
The issue isn't that you contacted someone via Facebook, I have contacted many exes through it. The problem is that you contacted a person you said you would never contact again. If you had never cheated and you husband left you over a Facebook message I would say he has jealousy or trust issues. This is not the same as contacting someone you had an affair with. Even if the FB message was completely benign it is still contact with someone you cheated with. FB is a communication medium, just like a phone call, letter, or face to face conversation. If someone calls, writes to or meets up with an ex and says the exact same thing as what was posted on FB it would be viewed as a betrayal, why not on FB? It isn't the fact a message was sent, it is that a message was sent to someone the OP had an affair with
after she said she would never contact him again.
There is nothing wrong with being friends with an ex if you are open, honest, and trustworthy. You are obviously none of those by your own admission.
On another note, why so people keep telling her (and other moms on these boards) to stop thinking about their needs? Yes, you should put your children needs infront of your own, but I can´t see how parents who disregard their own needs completely can make for good parents or role models.
I would never say stay in a bad or unhappy marriage. My parents did for years and the kids will know something is wrong. If you want out get out, but do not cheat. Once the marriage is over you can go find all the exes you want, but until the divorce is final there is no excuse for cheating.