I hope that you can find a way to stay with your bf. I think you will find things easier if you attempt the following:

Never criticize the bio mother to bf, son, or daughter.
Never criticize the daughter or son to your bf.

In other words, no use ever of terms such as crazy, delusional, liar, dramatic, attention-seeking.

If you make a mistake and use these terms, immediately apologize.

I make this suggestion because people will take an attack on the mother or daughter as attacks upon themselves--even if they can see the limitations of the mother or daughter.

I think there are ways to discuss behaviors without resorting to terms that carry with them an attack on personal dignity. I believe that you can find them and put them into practice.

With regard to the daughter wanting the attention of her father: Of course she wants that, all children want the attention of their parents. In my opinion she is not to be criticized or belittled for that: it is up to the adults to manage and guide those natural desires--not condemn them.