You're not being entitled. He's supposed to be your father, and he's acting like an utter waste garbage of a human being instead. I don't care about the technicalities, it doesn't matter if someone "worked hard" for their money, his virtue lies in how he's treated you since he took up the commitment to you and your siblings from the moment you were all born. Fatherhood isn't a volunteer job he can just cut off for the hot new thing in his life.
Unfortunately, from experience, there's nothing we can really do to change people like that. They chose to act the way they do, and think themselves above remorse. Society holds material wealth in too high of a regard, he will always think himself above everything as long as he has money. know that it's not your fault, the baby's fault, your sibling's fault. Your father is just a weak and self-obsessed person, and someone worthy of any sort of respect would know their wealth is best used to care for their own damn children if anything. If you're so filthy rich you can get your newfangled wife's baby gucci clothing they're gonna shit in, you can help your other child pay for necessities.
Let them live their empty, unpleasant, ugly lives, and when the time comes when your siblings no longer need your support in the matter, wash your hands of him.