I was wondering if I asked for his car, plus payments would they give it to me.
I seriously doubt they would award this in addition to child support as a form of supporting the child. Child support usually consists of a monetary payment.
Were you two married? If so, for how long? There is a slight chance that you could try to pursue the car as part of a spousal support agreement, but that depends on many factors (including length of marriage).
And also it would be very beneficial to her, because we travel to and from daycare VIA public/private transportation. Our bus stop is on a VERY busy intersection.
Many, many people are in the same boat, transporting kids on public transportation with busy intersections at stops or close to home. A car is not necessary for taking care of your daughter.
I am planning on suing for full custody before I file for support for our two yr old daughter.
Again are you married, and were you married at the time the child was born? If not, has paternity been legally established? If not, that will be one of your first steps.
Does the father want to have some share of custody or visitation? If so, please understand that he also has rights as the father. Now if he wants nothing to do with the child, that will not preclude him from paying child support. Visitation and child support are two separate issues.