When they realise it's not such a big deal and not as risky as the popular press like to make out they come round.
Ex Mrs CM used to be the same when I was picking up my kids (we were 200 miles by road apart at the time). She used to be very anti until one occasion when they were delayed back from a holiday, couldn't meet normally and I said I'd travel all the way to them to drop off the boys. When she realised that it meant she and new hubby didn't always have to meet me half way she now actively encourages it.
As for the kids - they just become very blase about it, especially when we discovered the game boy doesn't interfere with the nav kit