If you have a decent enough relationship with mom, why don't you ask her to meet you somewhere to do the exchange when she knows he's feeling clingy. I've experienced with my neices and nephews that it's a lot easier for a child to transfer at a place like McDonald's, etc. While the child is playing mom says by and dad takes over.
Another would be for her to hype the child up about 45 minutes before you or dad show up to get him. She could make it sound very exciting that he gets to go have fun with you. A 3 year old is very easily amused and will follow along with mom if she sounds real happy that he gets to go have fun. She could tell him she's just going to clean house, etc while he's gone so he doesn't think he'll miss out.
My son loves to be at home. Sometimes it was very difficult for him to leave his daily routine and go with dad. I tried these approaches and they worked. It didn't take long before he was out of that stage.
Also, it was around 3 that he became extremely close to my mother and actually called her mom and me by my first name for about 6 months. That was hard on me, but I put my money on it being a stage.
One other note. I think it was a bad choice for mom to make to have this get together knowing how the child has been feeling lately. It's not good on him, you, mom, dad or the guests that had to watch him cry. Mom should have walked him to the car to avoid a scene. IMO
I don't think there's anything you or dad can do to help this situation without mom's help.