I have a 22 yr old and I wouldn't want him to be stranded anywhere at any time, but especially at night.
If he called me because he needed a lift, I wouldn't hesitate, I'd just drive to wherever he was and pick him up.
However, asking me for a lift would be a last resort for DS and I know he would attempt to work it out for himself before asking me by either walking, getting the bus, cycling, getting a taxi or arranging a lift with a Co worker.
I have been in this position when DS was at college and he worked part time 16 miles away from home and finished twice a week after 11pm. This went on for a year before he found a job with more suitable hours and in that year, he asked me for a lift twice and I went and picked him up.
The only reason he asked me for a lift on those 2 occasions was because he couldn't get a lift from his Co worker and after sprinting 1.5 miles to the bus station, he missed the last bus home.
It is a shit feeling to know your child has just done a full day at college, walked 3 miles to work, worked a 6 hour shift then sprinted 1.5 miles and still missed the bus but DS would rather have done that than relied on me.
He doesn't like to rely on anyone unless it's unavoidable.
Perhaps your DD will learn to be more self sufficient in spite of her father?
It doesn't sound like your DH will change anytime soon so surely it's better all round for you and your DD to take steps to become as self sufficient as possible and therefore not need your DH as much as you both appear to now?
If you are even considering leaving this relationship at any point in the future, taking steps towards being independent of your DH can only be a good thing can't it? Perhaps you could take driving lessons. That is one avenue to go down so you don't have to rely on your DH as much.
It is truly horrible to be in a position where you have to rely on someone who cannot be relied upon. 