B, I wish we lived close by so I could give you a big hug, a cup of tea and lots of words of encouragement. I sense the most painful part right now is your boys being around OW and how it seems she is trying to take your place. Please know, that can never happen. There's only one, B.
OW can't hold a candle to you as a wife, a mom or a woman. Who know's why your H is with her at the moment, but whatever it is that R is all about him. She'll be working herself into a pretzel to please him and keep him. She sees how he has treated you. She could be next. She will be insecure and jealous of the family and life that you created with him. She won't have that.
B, your boys are likely trying to accept your H on his terms because they want his love and approval. It's too painful for them to be without. One thing I do believe is that the more people who love our kids the better off they will be. That doesn't mean OW, at least not right now. I haven't had to deal with OW yet, but the thought of it makes me sick. When she and xh were buying a house his attorney had the nerve to demand over night visits once a week. It really felt like I was being replaced in every way, like I was slowly being squeezed out. OW had my H, they were buying a home while trying to force a sale of mine and then they wanted to play family with my kids. I was hysterical. It was truly a low point.
Like you, my xh and I continued to use a joint account. He deposited my support and I paid the mortgage, etc. He also kept tabs on me which I didn't like. When my account was low he would offer extra money or criticize me depending on his mood. He used that knowledge as a reason to contact me. Once I opened an account in my own name I felt more secure.
You are wise to keep communication at a minimum for now. Things were so emotionally charged between you that a cooling off period will hopefully create some peace. When needed choose your response instead of reacting. I know, easier said than done. Like a teenager, your H is testing your boundaries and trying to get a reaction out of you. Stand firm and push back every time, kindly and lovingly. Through those actions trust and respect can be built. This is your edge, B. OW will have no boundaries. She is desperate. That will get old. You can be the calm in the storm. This is so hard. I have really struggled with this to the point I felt I needed to cut all communication so I coud get my bearings once again. We both can do this, for ourselves and our kids.