She might simply find out if the school has an after care option. When my SD was younger, her mom or then-SF would pick her up from there on their weekends and we never had to see her. We would give the after care people the basic schedule and try to inform them of any major changes. They had DH's number to call if they needed to confirm anything. SD needed care after school anyway, as DH was a single parent. The mom may want to look into PT options so that the child only goes on days where it's needed. If taking the kids to school is not part of the schedule, then he can do a quick drop off at the house or at a third party exchange area.
Or, change the time and place of the exchange. If the nanny doesn't want to deal with him, then make a meet up point somewhere public where the mom or a relative drives to meet him instead of the father going to the home to pick up the kids. Further, unless there is a real need, he can wait for the kids on the doorstep vs coming in and having much interaction with the adult who is home. Just have their bags ready to go. Things like that can minimize her interaction with him.
I would suggest to her that she find ways to deal with it because an exchange place may be stressful on the kids. The after care option would give the kids a chance to do HW, play, etc. and usually it's right at the school. So it's a place to exchange vs an exchange place. Follow?
ETA: http://www.occourts.org/directory/family-court-services/k...
It looks like at least in some areas, the service is free.