Wow- that's a lot to cope with. But remember- listening is not 'condoning' a behavior- but it is NECESSARY in order to really be informed about a situation before you decide how you feel about it.
When I got divorced, it was the most difficult choice I ever made. No one was cheating in my marriage- but there were many other pressures and things going on from my husband that no one else knew about. He was determained to present a perfect happy picture to all our friends and relatives and finally I just could no longer maintain that 'fake' picture for people and his issues came crashing down around our heads anyway.
I am not saying that is the situation with your friend- but unless you listen, you will never know. The one thing I will be forever grateful for is the way my friends and family rallied around me after I told them what was going on and that I was going to leave my husband. Even my parents, who did not approve of divorce, finally realized that in this case, the situation was never going to change and that it was the best thing for me and for their grandson.
Don't cast a stone- you just NEVER know what has happened in another person's life or what they need at any particular time. Many people, when in the process of getting divorced, see someone else, feeling that they 'deserve it' etc. But also- many women going through a divorce are so upset and so starved for someone to confirm that they are still attractive, a good person, a good mom, etc. that they behave differently than they normally would. I am not 'condoning' that- but I can see how it happens.
Be supportive about the issues you can be supportive about, and be candid and honest with your friend if you think she should not be involved with another man at this time- but do it out of love and support and kindness, not accusation, or from a 'holier than thou' perspective.
Your friend is dealing with this whole thing in the best way she can. Maybe it isn't how you or her family WISHES she would deal with it, or the best possible situation- but with love and support, she can make better choices for herself and her kids. Without love and support, she is only going to be worse, not better.
Good luck- remember, kindness and honesty are the best tools you have!