First, take care of your physical health. Eat well. Drink plenty of water. Go to bed at a reasonable and consistent hour, and if you can't sleep, just lie there and think about how good it feels to rest. Avoid alcohol and drugs. Take your vitamins and medicines. See your physician and ask about melatonin or other sleep aids or anxiety medicine if you think you need it. Keep up with your treatments.
If you have family and friends that you can trust, tell them what is going on and get them to help you with anything they can. Don't be afraid to reach out and ask for help. If they really love you, they will be wishing they could do more.
GET TESTED FOR STDs, AND DO NOT HAVE SEX WITH THIS MAN AGAIN UNTIL THERE IS NO DOUBT WHATSOEVER THAT HE IS COMPLETELY FAITHFUL AND HE HAS BROUGHT YOU A CLEAN BILL OF HEALTH. Which means certainly no sex with him for the foreseeable future and probably never again as long as you live.
You have cancer. If he throws an STD on top of that, it could easily kill you, and then the man who abandoned you right when you needed him and tried to manipulate you into screwing yourself in a divorce while you were dealing with cancer will get ALL of the money and will move one of the trashy sluts who helped him to betray you into YOUR home where they will congratulate each other on how well things worked out for them once the "bitch" died so conveniently.
Second, take care of your emotional health. Do 180, and do it HARD. Quit the "good talks". They're all lies and manipulation on his part. They aren't accomplishing anything whatsoever except to keep you in limbo so he has more time to find ways to shaft you. If he were the least bit sincere about reconciliation, he would have told you who she was or who they were. Unless you have a history of jealous violence, he has no excuse whatsoever to hide the truth from you, and his reason is that he is still cheating with her. I can just about guarantee you that.
Take some time for yourself if it is at all possible. Listen to music. Cuddle with your children or pets. Spend some time on a hobby you love. Read a good book. Go out for lunch with a friend and talk only about good things. Go to a museum or a concert or a silly tourist attraction that's nearby. Take a walk in the park. Buy yourself some perfume or a pretty scarf or something. Indulge yourself a little.
Silently whisper to yourself every single time you feel sad or lost or inadequate: I might not be perfect, but I will always be better than he deserves, and I will always deserve better than him.
Third, get your legal ducks in a row. Quit waiting on him. He has clearly decided to put off the divorce solely because of how much money it might cost him. He will keep you dangling on a string as long as it suits him and drop you the instant it doesn't, no matter what it does to you.
Try to get his promises to take care of you and your medical expenses as a signed statement. If he signs, take the statement to your lawyer; if he doesn't, you know he never meant it.
Document everything you can about his neglect, infidelity, and bad treatment. Be merciless. He certainly has been.
Get advice from your lawyer and do everything you can to protect your finances.
Fourth, accept that this man does not care for you.
I know that's hard. I know you don't want to believe it. I know you want to keep believing in the facade he presented in order to hook you. I know you would much rather believe the pretty illusion than face the ugly truth. But not only do you mean nothing to this man, I'm afraid that this man is most likely a sociopath or a psychopath who is incapable of truly caring about another human being. People like that are highly manipulative and utterly dangerous.
Any man who was capable of basic human decency would not have treated you the way this man has. I do not believe he is capable of remorse, and if I'm right, that means that there will NEVER be a reconciliation, just him using you until he thinks it's advantageous to discard you. This man is your mortal enemy, and the sooner you recognize that, the sooner you can crawl out of the pit you are in.
Get out before he destroys you. Please.
Fifth, you can wait for a positive identification that you might never get, you can talk to your lawyer about how to get the truth, or you can simply take what you have to the other spouse and tell him the truth: My husband has been cheating with someone at work. I think it's your wife, but I don't have ironclad proof. Here is what I have. Is there any way you can check on this stuff and verify anything for me?
Best of luck.