If the support order does not specify that the parent be the only person to pick up the children, he has the right to send someone in his stead.
Also, unless the order has a "First Right of Refusal" he can legally leave the kids with anyone he deems responsible during his parenting time.
You may want to ask your sister if the shoe were on the other foot. Yes, the whole new girlfriend thing sucks, but looking past that. Someday she will want to date someone, and if that person is important to her, she will include them in the lives of her kids. Anything she demands of him, will be also expected of her.
If I were her, I would ignore the absurdity of the situation unless the kids are in some sort of danger. Stuff like this in court can sometimes look petty.