Some very wise thoughts in this thread.
If you officially babysit Joey, even just once in the future, I think that gives you some leave to say to Paula, "While Joey was with me, he tried to do X, and I responded with Y. I just wanted to check with you that this was okay, and consistent with how you treat him." That might lead to a productive discussion. Though, as you say, when it comes to giving Paula advice I would err on the side of caution and NOT give it unless she explicitly asked. Of course, it also might lead nowhere--you'll have opened the door, but she has to be the one to step through it if she wants.
If Joey is making your interaction with Paula unpleasant for you (dinner, even just a conversation in the yard) I think you can acknowledge it, and end the interaction. "Well, seems like Joey needs you for something, I won't keep you. Have a nice day!" If this means you end up spending less time with Paula because of Joey's behavior (and her response), so be it.
As for teaching your child to stand up to a bully, I think you have it right when you said, "maybe the first step of equipping my kid to be strong is showing him when he's still small that he has the right to be protected by me." That is absolutely true. I often think of children being told to go off and play with someone, and quit making a fuss, the grown-ups are busy talking. Make sure your child knows that being quiet/nice does NOT mean he has to put up with bad treatment, and that you will take his concerns seriously.
And that he knows that just because Joey, or some future bully, is there in the neighborhood, that doesn't mean he has to put up with him, in the sense of playing with him. I always hated it when adults said, "Oh, you two need to play together, because you're the only girls and you're the same age," or "because you live so close," or "because you're cousins," or something like that. Yeah, it's nice when kids get along in those situations, but sometimes they don't, and forcing them to interact closely anyway can lead to trouble. Make it so that if your son says, "I don't like playing with Joey," your reaction is, "Okay, that's fine. How about we call Bob?" As your son gets older you can get into things like how to deal with bullies that you have to be around, like in class or at work, but let him know that his free time, and his home, are safe zones where he can escape from that.