I agree with secondtimearound's suggestion as well. It is frustrating for sure! I understand your POV but like you, I do think parents have the right to pick up when they need too.

When does he get the call and know that he needs to pick up early? Can he text/call you when he knows so that you don't put her down for a nap or can you put her down for a nap somewhere else? Even on the floor in your bedroom? If he doesn't pick up early, can mom pick up or is past your closing time?