Lol, you are so TA. Her mother a ESH.

You paid for your step daughter to have a car and the gas/insurance but you won’t pay for your own biological child’s car situation?

Are you listening to yourself?

The car will be hers and will help her immensely regardless of where she is majority of the time.

You’re her parent and it is your responsibility to help 50% , nobody can force you to do anything but your logic on this is way off and I suspect you know it is but just don’t want to do it.

Only thing I can agree with you on is the fact your ex wife is being ridiculous.

Also , your daughter probably has said something , just not to you or her step sister.

Step up and parent both kids equally regardless of one or the others circumstances before your bio child cuts you out of her life completely.