Gen xer, I like your word "overstayer"! My wife often is an overstayer, especially when we're visiting her family. It's odd, she is almost always late arriving at these events, but once she is there she usually hates to leave.
To be fair, we are usually very busy and she does cherish her time to relax with these people she loves so much. But sometimes I start feeling uncomfortable, such as where our hosts look very tired, we're the last or almost the last guests there, and then our hosts start yawning...
And when our kids were younger they would often (but not always) get bored at her family gatherings, especially if there were no other kids to play with there.
So, if we all went in the same car, I would try to negotiate ahead of time a time when we would leave. If my wife had agreed upon a time, I'd go ahead and start getting the kids ready after the agreed-upon time, load up our car, and then say good-bye to everyone and then ask my wife to join us in the car. The kids and I would wait in the car anywhere from five to twenty more minutes for my wife to say all of her long good-byes, but eventually she would come to the car and we would leave (usually 30 to 60 minutes after the agreed-upon time).
I'll admit there were a few times when she just would not come out to the car to leave with us. After 15 or twenty minutes I'd go back inside and whisper to her that it was time to leave now. If another 10 or 15 minutes would go by, I actually once or twice went inside and asked another relative who lived near us if he would give Mrs. Snappy a ride home if I went ahead and took the kids home myself. (I never left Mrs. Snappy behind without a ride arranged and always only if she agreed to the arrangement.)
What was much easier for us was when we would take separate cars to her family's parties. I could arrive on time and she could be as late as she wanted. I could leave after four or five hours (with the kids, usually) and she could stay until she was the last guest there (as she often was). Everyone was happy.
Taking two cars is harder to do now because gasoline is more expensive and our finances are tighter, but that surely was easier for us!
OP, I take it you live so far away that asking another relative to give your husband a ride is not possible?
I agree that this can be very frustrating, and when it would happen when we had only one car, I would feel guilty about wanting Mrs. Snappy to keep her promises about departure times. Then again, Mrs. Snappy was showing the kids and me disrespect by not keeping those promises, wasn't she? (Two cars really was better when we could do that!)