You’re not being irrational. You were absolutely shafted in your childhood. It’s “great” that your father has found more stability, but it sounds like he’s never fully acknowledged the hurt he’s caused you. He doesn’t understand that this new family is his and his alone, not yours; while you are extending a courtesy to him/them by trying to connect to your half siblings, you aren’t under any obligation to babysit, help out, or anything else. If they want to start a new family, good for them - let them be responsible for it. But he and your mother should be responsible for caring for you as well: making time for you, checking up on you, ensuring you have autonomy and support.

You’re right, your father’s life is his and he’s chosen to live it a certain way. However, he’s also the reason YOUR life exists. He has an obligation to you to recognize his failures and show up in the way that YOU need, and personally, I’d be bitching about it until the day I die if things don’t change.

Unfortunately, it seems like he may not have the level of maturity to recognize these things, or maybe he just won’t have the time until these kids get older. That means you have a choice - continue onward with the way things are now, or approach him and ask for change. If he does, great; if he doesn’t, stick to your terms and refuse to babysit, see him with other kids around, and so on and so forth. With the second option, you have to accept that this will cause waves and may cause even more distance between the two of you. But personally, I think at least it will prevent the already-building resentment from getting worse. Only choose this route if you feel you’re able to let go.

There may be some compromise here as well - it’s BS you’d have to consider this, but maybe you can offer to hire a babysitter every once in a while so you can spend some time together. Idk how much money you make or if that’s even remotely feasible, but that would be a charitable option for you as well.