He sounds delightful. Seriously, he's more concerned with his girlfriend and her child than with your need to support yourself and your/his child? Your work schedule should not have been discussed with your daughter by him. That's ridiculous. And it's even more ridiculous that his girlfriend arranged custody with her ex based on her new boyfriend. No mature person would do that.
It's not selfish for you to make more money. Your child will need braces and college and summer camp and whatever else (fill in the blank). If he's a bully in other ways (perhaps that is why you are divorced?) then please work with a counselor to help you strengthen your own boundaries and ways to say what needs to be said without feeling intimidated. A good therapist can actually help you role play and rehearse. You could also try a family counselor (if he'll go) to work on coparenting. Sometimes an objective and neutral person can help you avoid problematic encounters with just him. If necessary, you can get a mediator through the courts and your ex can plan on paying more to fight you.
It would be nice if your daughter were raised to be a strong person who understands that sometimes we have to adapt to life's curve balls and make adjustments, that things aren't always convenient, and that sometimes change is good. Your ex is getting in the way of that. Maybe he expects that everyone will accommodate to what he wants (you, his girlfriend, your daughter, the girlfriend's ex) but that's pretty juvenile.
I have a friend with a real idiot ex (moved to a new state, can't get or keep a job in part because he chose an area with a floundering economy, and now has lost 2 houses and is living in a trailer). He rarely sees the kids but yells at her about her interfering in visitation - even though she offers more time and he never takes it. One child has been in the ER 4 times for severe mental health crises, and the dad has never come. And more. She basically texts or emails him rather than meet with him, so she has a written record of his refusals and rants. On phone calls with school psychologist or physicians, she puts him on speaker so he's included but others can hear what he says. It's not ideal, but you can't coparent with someone who won't coparent. So I'm not sure you can make your ex into a coparent. You may need outside help.