I am in a sort of similar situation. And I am back again. I suspect my M is done. He is with XW1 and left me with our 4 kids. It seems so easy for me to tell someone else what to do. Impossible for me to do it myself. First, if you did DB before then you know you are doing everything wrong.
1. Set boundaries. Tell him what you expect and what will happen if it doesn't happen. If you are open to reconciliation then you need to stay what you need for that to happen. If you cannot even entertain the idea with OW involved then don't accept that.
2. I completely understand feeling relieved that he is gone on some level. I also understand that it is MUCH harder on you and you do have to be a caretaker to all those kids. There is little time left for you. I have actually been doing more activities with my children. We do the library on Sat mornings and free or cheap community activities fairly often. They are playing basketball and doing that sort of thing so it keeps me busy and I get out of the house. Consider these types of GAL activities.
3. IGNORE THAT W!TCH. Do NOT talk to her. No reason to. She is nothing to you. Certainly there is no reason at all for you to listen. She wants to laugh at you? Ha, laugh back. What kind of stupid twit gets involved with a man that has to pay child support for 6 kids? Is she planning on supporting him? Is it really THAT great? I doubt it. Of course, don't say that.
She only gets and hears what he wants her to. And my thoughts on that same as my own H OW- What kind of real woman wants a philandering cheater? None. Soon the sex becomes routine and they get bored. Then they start to notice the other things like morning breath the horrible family and things fall apart. You have been through this multiple times before you should KNOW this.
Of course this is not your fault. Perhaps the problems in your relationship leading up to this you have a hand in. Most certainly you do but the cheating? Nope. Not at ALL your fault.
4. Set up visitation and child support. Depending on your location you may be able to get child support started just by going into the local office. (this is to protect you and your kids)
5. My H has changed in the past for OW then reverts right back to the same jerky ways for me. You know why? Because I settle for that. That's why. When I quit accepting it, he will stop doing it.
6. You need to sit down and really really think about what you want in a M and if your H can reasonably be that guy.
For me- I know my H cannot. At least not without divine intervention that will truly change his heart.
In truth, despite knowing all of this it kills me every time I talk to him. It is like a knife in the gut. Unlike any pain I have ever known before. I really cannot even begin to fathom how you have gone through this 4 times.
I'm so sorry for your pain.

Please work on no contact and GAL. You CAN do this if you want to. But more importantly, this needs to be the last time. So either you change and demand he treat you as you should be and he comes back with real consequences and really tries to change and focus on M or you decide you can't do this and still move on in a better place.