From a principle point of view, I personally think the one that causes the extra travel time and expense should be the one to take care of it. So honestly, I think your husband should be doing the extra driving each way.
Legally what kind of position would you be in.. depends. In my state, WA, anytime you move out of your child's school district, you have to send the other party written notification, and technically the other party could object and request a change of custody.
If it was just the next city over, the court isn't going to make any changes, except maybe specify the change in pick ups and drop offs.
In our case, my husband's ex had moved his daughter two counties away, about an hour and a half each way (three hours travel every other Friday sucked!) Initially the recommendation was that mom would be required to pick up and drop off every weekend she was with us. Then it got changed to the receiving party picked up. So someone traveled 3 hours on Fridays, and 3 hours on Sunday.
She now has moved out of state. Our laws here say the travel expenses are split in the same % of the child support order, unless there is a good reason for a deviation.
Some states don't have any such law. Then it's decided according to case law, if there is any, but mostly at the judges discretion.
How much time share does she have in the summers? Maybe you could give away some more of your time share in exchange for a once a month visit and you do all the driving.
Hopefully you all can come up with a creative solution that can keep you out of court.
For my husband, when his daughter was moved that far away, it meant that the mid week visits were almost never possible because he got back from work too late to have time enough to even get there on time. It also meant that he no longer could see her soccer practices. It really sucked and deteriorated their relationship just due to the fact that they didn't have as frequent face to face contact, even if it was only for a little while during the week.