Is that about right mike? I have inferred some things I know...
I think the thing is some things that she is doing are not right and some you are doing are not right, most are understandable given the situation (living arrangements, ages, your other child etc).
I can certainly see why it would be distressing for you to not be seeing your baby after seeing her all the time then find out ex has had a night out without baby but that’s one of those things you have to try and suck up.
I can also see why her laughing at you when you were upset would also be very distressing but she is very young and possibly immature again something you need to try and not react to.
I can also see why if you were in a relationship she wanted you to stay at home with her as a family and why she didn’t want the baby to stay overnight without her when she was only 2 weeks old.
One of you has to break the cycle of pettiness. Since you are the one that has come here, you are the one who is going to be advised that it should be you.
What is important is for you now to be trying to establish an agreement about the contact you can have going forward as separated parents.
If you’ve ended the relationship very recently then it is possible you will need to allow time for the dust to settle first.