Update!! (All the way to the bottom) I need your honest opinions

Back story: I was with my children (girls; 17 yrs and 6yrs) father for a very very long time. I found out 2yrs ago that he had another child from “a one night stand.” I was in complete shook and denial that I continued the relationship for another few months. BD showed up for my youngest’s bday with this child that we had all just found out about; he gave me no warning or anything. I contained my emotions and kept hosting because it was not the place or time.

Fast forward to now: Emotions have been kept in check and this child has been brought to any event that has to do with his sisters. Well, my oldest has finally let the cap off and has let her father know that she does not wish to have her half brother at her birthday coming up. He blew up getting upset at me and saying that I’m the one putting a wedge between his children. He went off on her and even gave her an ultimatum; either she allows her brother to attend or he (dad) will not show up at all. So my daughter being the hard ass that she is told him straight to his face “THEN DONT COME.”

These past 2 yrs it’s been hard for me because around the same time I found out about this child, I was going through a miscarriage. I have put his (BD) feelings above all but not anymore. I backed my daughter and stood my ground with BD. He states that I hate his son and that I’m going to regret putting a wedge between his kids.

Ladies tell me what you think of this situation. Ask questions if you like, I’ll give you guys as much info as I can.

Edit (Answers to Questions in Comments):

-He cheated.

Update:

He showed up for the birthday; an hour late. Sulked around, sat by himself in a corner looking for attention from my family (which they ignored). You can feel the tension in the air. Then would walk past by where I was just to see what I was doing or with whom I was talking to. And once he realized that whatever intentions had had planned was not working, he decided to leave before we sang “Happy birthday”. He was a child and everyone noticed.