You aren't just being unreasonable, you are being ridiculous.
It is perfectly normal for working partners to support non-working partners while they study or while their employment position is unstable. That is what normal partners do. So get over the fact that your dad supports his wife because by doing that, he is doing the right thing. Stop being ridiculous. Give it up, its hurting you and no-one else.
It isn't your business whether your father's wife works or not. Their arrangement has to suit them, not you.
Your dad and his wife aren't obliged to live their lives the way your mum and your step-dad do. To expect that is unreasonable. Stop having unreasonable expectations, then you won't have to feel bad about those expectations not being met.
About your dad and his lack of support for you and your mum - he was unreasonable in that. It was his responsibility, not his present wife's. He should have provided financial, practical and emotional support as part as his duty as a father - but he didn't. A lot of people don't. You have chosen to have contact with this man, knowing exactly what he was like. Your choice. To object to him being himself, now, is unreasonable.
Your dad's wife was unreasonable in verbally abusing you and saying hurtful things. Very unreasonable. Dislike her for that. She did it, it wasn't right.
I don't know how far your dad being a useless father influenced your choice of another useless man to be the father of your child. But if you did that, it wasn't anyone's fault, as such. You could have accessed counselling before conception and made a better choice, but people don't always do the best thing for themselves. But it is not your step-mother's fault, or even your dad's.
OK, maybe on consideration, you aren't being 'ridiculous' in every aspect of this. But you are being unreasonable to lump it all together and blame the woman for everything.
Stop trying to blame other people for your own problems. Focus on your own life and your own issues - get help for them and enjoy your life with your child.