It is not an ultimatum -- you are not saying he cannot live his life the way he wants it. He can go on all he wants.
It is not an ultimatum to think about leaving a situation that YOU do not want to be in. Because you can live your life the way YOU want. Because you deserve to be treated nicely. You have dignity, worth, and value.
You have the RIGHT to live your life in a way that feeds you. You choose who you want to be with.
You want a monogamous romantic relationship. He will not provide that. (There's also a whole bunch more weird there.) Therefore you cannot be in a romantic relationship with him. That is about it.
My sister has flown with her baby a lot more than I did with my kid -- but she went with her spouse so they could take turns holding him. It might be worth getting two seats so you can put baby in a proper baby carrier so your arms get a break. It is free to call airline and get info, so why not check it out? Just to really look at the option before dismissing it.
Since you are not given access to finances?
Could also call Nevada DC
F (You are las vegas right?) to see if there is "leaving aid" available in your situation. You have a place to go, right? Your parents. So some help getting there would be great if you are struggling with cost.
Could also maybe call up some churches?
Sometimes the minister has "minister discretionary funds" to be spent however the minister deems fit. Once you land with the parents and are better settled in your new life you can make your thanks and repay/donate funds to help some other person in that community out of a bind. I know my UU church gives the minister funds for the "minister discretionary fund."
Just some ideas -- again, free to call to ask for information. You aren't hurting anyone by seeking info. Maybe other readers have more ideas.
It's good you talked to your parents. Hang in there!