Blaming it on insurance is a good excuse saying once you have picked up your child I can not be responsible for you still being in my yard. Please use the park down the street - and don't forget to take your car with you (wouldn't want them to just walk,lol).
Use the excuse that you need the parking spot for another parent and he needs to vacate it as quickly as he can.
I have had a parent come and hang out when we are out back playing at end of day saying other spouse was making supper and they are putting in time so it will be ready as soon as they get home so they don't have to deal with the child whining for food - considering child is busy playing and not whining when they are telling me this - well hard to have sympathy knowing it is just a learned game.