There were quite a few times when my boys and I cried together too. It is incredibly painful knowing that there's nothing you can do to put your family back together. I remember begging my H to come home for the boys. The response I got was "I decided the day I left I would never put them first again. I did that for years and I was unhappy." I was so shocked I immediately wrote it down and dated it. Several days later he denied he ever said that and called me crazy.
The boys were told all kinds of excuses for why my H left including "Mom makes rules and then breaks them." I couldn't believe it and had no idea what he was referring to. My H used to tease me about being too much of a rule follower. There is a reason it's advised to not believe anything that they say. It's crazy making.
You and the boys will start to heal and create a new family with new routines and experiences. Last summer we took a lot of day trips, mostly to the beach. Those outings were so good for our souls. At first it always felt like someone was missing, but gradually we started accepting that our family had changed.
I also did what I could to create a soul nourishing environment at home. I bought fresh flowers weekly, burned lots of candles and played music regularly. Those simple things made a world of difference to the three of us.
You'll find the things that help you and the boys along. It takes time. Even after six months it was still very difficult or us. We gradually started turning a corner. I felt a lot of pressure to get myself in order. I knew the boys were anxious because I was so sad. More than anything they just wanted a happy Mom. Eventually I decided that I was going to give them the very best childhood I could under the circumstances.
I know this is incredibly hard. I can't even imagine how it must feel to have the OW around your kids. Set boundaries with your H regarding the boys. Do the best you can to protect their hearts and minds. That's difficult since you're dealing with an incredibly selfish person right now. As their mom you do have a say in how you want the boys to be raised and what is not ok with you. If your H is doing something that's not in the boys best interest, firmly let him know. He may view it as controlling, but too bad. I let my H know early on that when he spent time with the boys it was about them. He was not to bring up our marriage, the divorce, finances and especially not his gf. He did abide by that, thankfully, and so did I. Maybe the two of you can talk about what your boys can handle and what the off-limit subjects are.
B, know that you and the boys will be ok. There's a lot to deal with right now, emotionally and logistically. Take it a day at a time. As hard as it is try to remember what you've learned about MLC and the unresolved issues that lead to the crisis. Try to remember that somewhere inside your H is a hurting child who needs compassion. It will help diffuse the anger.