My WW has commented that she wants to be over and done with this whole situation, just move on.
This does not sound like a woman who understands or cares that she has hurt you deeply and possibly damaged her marriage beyond repair. This does not sound like a woman who is going to accept any accountability for her actions. This does not sound like a woman who feels a shred of remorse for what she did to you, your children, your families, your marriage, your sanity. This does not sound like a woman who cares about you or your feelings.
I'm sorry to be so brutal, but that's what I see.
I see something else. If you're doing all that monitoring, then you clearly have no trust left in her, and she isn't doing a single thing to reestablish it that I've heard about.
You're checking for chat and message accounts that use her email address? It takes just a few minutes to set up a new email address. She could have dozens you know nothing about, and she could use those email accounts to open other Facebook, Twitter, and other accounts. As for phones, burner phones are cheap. They have lots of ways to stay in touch.
GET TESTED FOR STDS. DO NOT HAVE SEX WITH HER AGAIN UNTIL YOU HAVE CONFIDENCE THAT SHE WILL NOT HAVE SEX WITH ANOTHER MAN AGAIN. PLEASE.
If you have sex with her again when you clearly feel you have no reason to trust her, she has shown no remorse, and instead of working to repair the damage she did, she just wants you to get over it, you are putting yourself at risk every single time you do.
You should most definitely see a counsellor, but it should be a legal counsellor. Find a lawyer. Protect yourself. Protect your children. Protect your finances because that is how you are going to be able to take care of your children. Don't tell her that you are going to see a lawyer, just do it. Save evidence. Start an electronic diary that is encrypted with a password she won't guess and document everything that has happened and every suspicious thing she has done. You never know when it might become essential.
You should probably set up your own individual bank accounts. If you have direct deposit, set it up to go to your individual accounts. Don't clean out the joint accounts, but you can probably safely take half. Ask your lawyer for advice about it. Store your essential records in a safe place she cannot access. Make copies of important records and get a family member or friend to hold onto them.
I hate that you are having to go through this.
I understand that when you have been married for so long, it can be hard to let go of that investment, but instead of asking whether you can save your marriage, you need to take a realistic look at what she did and ask yourself whether that is really the person you want to spend the rest of your life with. If a woman did that to your son, would you want him to just forgive her and move on so she could continue to enjoy financial stability?
I think you should start operating on the assumption that the marriage is over. If she is truly capable of remorse, you can reconcile later, but if you do not take steps to protect yourself legally and financially RIGHT NOW, you could be screwing yourself.
Best of luck to you.