I have one daughter that lives in 45 minutes from me and I'm unable to have reliable transportation to pick her up and get her back. Does her father hold some kind of responsibility in my visitation

Normally no. I will have to assume the father has custody of daughter and you have visitation.

Have you talked to him and asked him?

What the father has to do, is outlined in the custody and visitation agreement

The only resposibility he has as far as visitation is that if it is court ordered he needs to be following the court orders. So if you have court ordered custody his obligation is to have the child available for that custody.

Generally no. Transportation is up to the NCP. The custodial parent has to make the child available for pick up at the designated times. I don't know exactly what your visitation order says (and I'm not asking). So what you need to do is go look at the paperwork from the court outlining the visitation and see if it says that the father is to meet you somewhere half way or bring you the child. If not, then it is your responsibility to go to the child (again that is more normal). Have you talked to the child's father and told him the problem you are having in getting there?