Sorry for this family problem, it sounds hard! I would be hurt by false allegations about my child whom I adore. For sure. But I have to ask you, what do you think her motive would be to make this up? With so many kids around, could your 9 year old have repeated something another has said in front of him or something he's seen? I think I'd have had a serious talk with my son wanting him to telling me the truth and knowing that this is tricky with kids so also trying to talk about things that he needs to be aware of (like what is okay to say and do with other kids and what isn't--- and if anyone has ever done that with him, he needs to feel safe to tell you).
In reality, her reaction while a bit much is probably what most parents would do if they were believing in their heart that the other child said/did things. And it is in everyone (including your son's) that he not be alone with her child again because if they are false allegations, you don't want more made. Your son is safer not around her kid if her kid is accusing of things that didn't happen. It's awkward because of family but it is what it is. I would do your best to find a way to have a relationship and time with her kids so they don't suffer. Will she bring her kids around with the whole family there?