I’m so sorry you are facing THIS horrific - as if the actual affair isn’t bad enough.
I was in your shoes and I watched my H do exactly what your H is doing.
Unfortunately my H chose to start the affair for a second time after it being "over" for about a month. He had this "I deserve to be happy" mentality and literally became a selfish jerk who was planning to D me to be with the OW (other woman).
Since you don’t know where the marriage will end up, I suggest you start to financially protect yourself. Get copies of all financial documents - tax returns, bank statements, retirement accounts etc.
Also read up on the 180. Stop being his wife until he really truly commits to the marriage. You may think this is being mean but it is actually designed to shield yourself from being subjected to his continued cheating — even if not physical, in his mind the OW is "first" right now.
Let him wallow in his shame and unhappiness. Do not support him. Honestly he’s lucky he has a place to call home right now. If I had to do it again I would have kicked my H to the curb during his "missing the OW" phase.
Get yourself some professional advice as well. It will help you navigate this situation and provide some support for YOU.
Please keep posting here. You will get great advice.
From experience I would suggest that you do nothing about your marriage right now. Your cheating H is not interested and it will be a waste of time. I would also suggest that you have a firm deadline w/ the eye towards how long you will allow this behavior from your H to continue.
You do not have to accept this from him. You can (and should) decide what is best for you. When I found out my H had restarted the affair, I was forced to pull the plug on the marriage and plan to D him.
That was his wake up call. And while we are happily reconciled, he’s now afraid I will D him!
There is a book your H should read - How to Help your Spouse Heal from Your Affair by Linda MacDonald. If he refuses to read it, there is an indication that he’s not all in on the marriage. Many cheaters refuse to read it - and to me it’s a clear sign of where they are and what their priority is. To me it’s a red flag 🚩 🚩🚩 unless they are doing other things to make amends.
Learn the difference between remorse and regret. Regret is they are sorry they were caught cheating but don’t regret it. Remorse is they are sorry cheater feels bad for cheating and is willing to do anything to fix it.