Separation anxiety is a big deal with children. Mom could do everything right and the children would cry and otherwise physically exhibit their emotions. You have to admit, there are some powerful emotions on each side of the doorway when it's time for visitation to begin or to end.
Routine helps ease the transition. Try establishing a routine that when they leave with Dad, they are headed to the DQ. Give them a few minutes to accept the transition and have some ice cream (not a meal). Then, they should be more willing to complete the trip to Dad's. A lot of parents have this type of interaction with their children and find it helps to calm everyone's nerves and get visitation off to a good start.
Mom certainly can't guarantee that the kids won't cry when they leave home or that they won't say they don't want to go; and, neither can a court.
Children didn't arrive in this world equipped to handle the demands of visitation. It is an unfair burden we have placed on them.