Why aren't you setting boundaries? Why are you leaving it to the other mother to "recognize boundaries?"
I would be very clear with House Rules for the younger rambunctious child.
"We don't hurt/antagonize our pets in this house. If you don't stop I'm going to ask your mother to take you home right away. You have one more chance." You say this firmly in front of the other mom. Then you have to follow through.
At drop off: "I'm sorry, Rita, but I don't have a lot of time to socialize this afternoon. I have a lot of things that I need to get done in a short period time otherwise I would sit and chat."
After a few minutes: "It's been nice chatting and catching up, and I hate to make you feel as if I'm rushing you out, but I have to take care of ___, ___, and ____ while the boys are busy. I'll see you at a ___ pick up time, ok?"
At drop off: "It's so nice to see you. I need to let you know that Jack can only stay until _____ tonight. If you can't pick him up at ____ then I'm going to have to drop him off at your house myself or have my husband do it."
At pick up: "The boys had such a great time! We'll have to do this again on _____ (a couple of days away). Thanks so much for coming over today. It's time to get the kids to family dinner and then homework but we'll talk later?"