My brother is having a mental health crisis and I'm resentful of my dad supporting him.
For what reason would you resent your dad being supportive?
Because my brother is so ungrateful.
It's expected that parents will help out their kids when they are experiencing a problem and especially so if that problem is related to mental health. You shouldn't resent your dad trying to help out, even if you think your brother is ungrateful for that help, since your dad was trying to do his best as a father. If you find your dad's actions to be upsetting, you should try to talk with him and discuss how you worry about him being taken advantage of by your brother.
I've tried to talk to my dad about my brother's traits and he won't listen. I'm just going to ignore him, sometimes I feel like my dad is the worst.
Your dad isn't the worst and like him you should be more supportive of your brother, as he's struggling mentally. It's your dad's responsibility to help your brother and you should try to see the big picture and be more understanding and empathetic to both your dad and brother.