Yes, I do remember your situation. And thanks for requesting to talk with me again. I am glad to be able to help.
It certainly sounds like your mother has some issues going on.
If she ignored the suggestion of therapy, then she may either be scared to go with you, or she does not want to. But any attempt to try to work on the relationship should be met with some interest by her. If she ignores you, that is not a good sign about how she feels.
Your mother needs to visit without her boyfriend at this point. It should be obvious to her that you and your family are not ready to meet with her boyfriend or accept her life choices right now. Your family needs her attention and those damaged relationships need to be repaired before other people, like a boyfriend, are brought in. If your mother tries to bring in a boyfriend at this point, it is only going to cause more friction and more heartache.
And the fact that she is trying to do this right nearby your father is not good, either. Stirring up trouble and trying to hurt your father is not going to help things. It leaves you and your family to take sides, and that is not in her favor, either.
If she was willing to work with you on these problems it might be a good idea to try to stay in contact with her. But if you feel she is only doing these things for her own advantage, then it may be a good idea to back off for a while and give her space. If she contacts you, let her know that you are busy and cannot deal with the situation for now. Then leave it at that. This gives you time to step out of the situation and get a break to think things through. But it also leaves a door open in case you think it all through and change your mind about trying again with your mom.
Let me know what you think,