S.O.
I would get them some councelling. I would also back off of your relationship with your boyfriend in front of the children. They are in turmoil, and they need you right now, and you need to put your focus on them, and making sure that they are alright.
Trust me, I am not speaking from a high horse, I am speaking from experience.
My two oldest girls live with their father. They are 13 and 10. Not only were they unhappy with my new relationship, but it was fueled by thier father, who doesn't want to see me happy, but what it really all came down to, is they wanted me.
When they act out like that, it's a cry for help, not only professionally, but for you.
I now understand that my happiness doesn't matter as much as theirs, and that when I decided to have children, I made a commitment to them above anybody else, and I didn't see that. All I saw was why can't I be happy, and what about me.
My 13 year old will not even talk to me right now, because she feels like she was abandoned.
They only want us around for a short time, and then they don't, just like that. I wish I would have held her more, and read her more stories, and just listened to her.
If this man loves you, than he will back off, and not force himself into their lives. Let the wounds between you heal, and over time they will.
Get a babysitter twice a month, and go out with your boyfriend, but keep it seperate, and one day, they will be ready for you to have one.
You can hear what I say or not, but there is a hole in my heart where I wish my daughter was.