I agree with a suggestion that has worked like a charm in our situation: the receiving parent picks up. However in our situation, a custody evaluator has it set up that all transitions happen at school which isn't always the best, and am not suggesting husband and ex wife attempt to change their visitation schedule. However, if the court order can be modified to the receiving parent picks the child up at the beginning of the visitation time, bickering will stop...and also include, after hashing out first, what works as far as when its OK to drop the child off at school...just make sure its in the order.
In the meantime, dad should follow the order to a T. Then file for a modification. Keep it simple.
Not to fuel any flames, I keep hearing about moms' drinking. Just me, IF I were dad, I would not make it the issue in court, but I would have my attorney help me out in bringing it up, if he has sincere concerns about mom drinking and driving with kid in the car. Not saying it will go anywhere, but I would feel remiss if I had that info and didn't bring it up.
Another tip of something that got included in our court order that helped us a lot, is we correspond by email. That way you have a paper trail of disputes around the court order...ex. mom refusing to cooperate around transportation.