He did confess to me though that when he gets mad at me he does think of cheating on me with her or other women just to get back at me, and that he contacts her through msgs or hangs out with her because it would piss me off
This is extremely unhealthy. Instead of discussing problems with you, he just decides to get back at you? This is a recipe for disaster. He'll need to keep upping his game to get to you. This is NOT how problems are solved in an adult relationship. I'm sorry, but he sounds extremely juvenile. If you don't mind my asking, how old is he? His thinking is not that of someone that wants a good relationship.
You have a child with him, and another on the way. I suggest you try counseling together. He may be against it, but his method of coping with upsets is very bad and he needs to change that.
You also mentioned he thinks you'd cheat with your daughter's father. He sounds very insecure. Has he always been this way (insecure)?
Regarding his father - a death, particularly of a close relative or friend, can make people feel as if life is going to pass them by. It can make people 'snap', so to speak. I don't think this has a thing to do with his father's wish that he dated more women, and it's not an excuse for anything he's doing. The fact that his behaviors changed after his father's death only reinforces my belief that counseling should be considered.
I don't know why your daughter's father isn't in her life, but that's hard. You have another child, which is hard. You're pregnant, which makes anything more difficult, and is challenging by itself. Your BF should be supporting you right now, not purposely behaving in ways that will upset you.
If he refuses counseling, then the ball is in your court. With two young ones and another on the way, I'm sure this is scary, but your BF can only do this for as long as you are with him. You have the power to stop this, at any time.
Your daughters are learning what to expect from a relationship from you and your BF. Please teach them to accept nothing less than respect. You don't want this for them in 20 years.