Complaint about another family in my childcare centre....

How strange is it that some kids just get buck-wild at pick up time??
It sounds like you need to become "the Enforcer" now. Do not allow this to happen, as it is disruptive to you and the other kids, not to mention teaching the other kids some bad habits.
My contract states that once a parent arrives, THEY are in charge of thier children, but MY rules are to be enforced. If this does not happen, I will step in.
I used to have a school aged child who was ridiculously spoiled, and would become a whiny little devil child when mom or dad arrived. I don't know if it was embarrassment or reeeeaallllly laid back parenting, but the things he said and did would NOT be tolerated from my kids! The day he kicked my front door because he didn't like what they were having for supper, I was DONE. From that point, I would nip that behaviour in the bud whether parents were there or not.
Maybe it's time to send out a newsletter with drop off and pick up expectations? Remind parents that you are looking after other children, so do not have the ability to spend more than a couple of minutes at the door during these times. Any important issues be discussed at a time more convenient for everyone. When mom/dad arrive, it is imperative that the children understand that it is home time, and that they will come back the next day, etc.
Sometimes I think we as providers forget that people treat us, our home, our schedule, etc exactly how we allow them to. We need to remember that (to a large extent) WE are making the rules here!!

OMG'sh, just a quick story about a set of twins I had for 2 weeks tops and then I terminated. 3 year old idential twin boys, were a major handful while with me and even worse when the parents showed up. They spent so much time in time out at my house it was crazy. Anyhow, one night in particular, mom showed up to pick them up, its winter so they need all their stuff, 1 would refuse to let me help him, mom had to do it, if I did hed take it all off again and wait for mom. So this one night, she is helping him, he's screaming at her and laughing at his brother who is running full tilt around my house screaming and laughing bc he didnt want to go home. I caught him several times and took him back to mom but off hed go again. Once twin #1 (the one who refused help from me) was dressed, she dressed twin #2 as #1 undressed himself again and took off to tear around the house again, I guess he thought it was funny that I had to chase and catch his brother and wanted in on it. Despite threats from his mom, he continued. Went on like this for Id say half an hour and finally, both boys were dressed, she with one in her arms and me with the other finally got them out to her car! Insane!! INSANE!!!!!