Your "off track" was a little revealing, and I think you have some resentment going on. This may affect your judgment on what you think is "fair" in this situation.
Typically, the court will say that if one parent moves, it is their responsibility to arrange for transportation at visitation. It does not matter what county either of you live in, but the distance between the non-custodial parent and the custodial parent's place of residence is the issue.
I guess when Mom moved 20 miles away from where she had lived before your husband simply adjusted the time that worked out equally for each of them. Now that he has moved he feels that the same adjustments should be made by mom. Bottom line - if mom is ordered to drive daughter to dad's, then drive she must. If she gets her license suspended, she must still find a way to provide transportation for her daughter to visitation. Most people, however, are not willing to go to the expense to insist on these issues.
The important thing is that dad continues his relationship with his daughter. How mom reacts, how hurt you are from her behavior, how resentful dad is about the lost license issue - none of that matters as much as the relationship between dad and kiddo.
My suggestion would be that you do what you can to facilitate the visitation. Offer to take the girl home with you from work. It won't really hurt you, and you will feel good about your contribution. If Mom yelps about the extra miles, dad could remind her of her license being lapsed and how he could have brought her up for contempt. Maybe that will help calm the waters.