Would this be appropriate or is it completely out of the question? -- Background first, question at the end

Our friend (I'll call him John), has a 4 year old son (I'll call him Kyle). Kyle and his BM -- who has primary custody -- live just down the block from us, and we all live near a playground/park. The BM is one of those who will never budge or alter her arrangement with John and would rather her son not have any relationship at all with John. She only allows John the minimum amount of visitation that she is court-ordered to give.

(Just to add in there that John is a good guy who 'messed up' -- cheated on the BM, but is now married happily and has 2 daughters with the woman he cheated with...so obviously that's the source of all the resentment. However, he's a great dad, he WANTS to be involved, he WANTS to have Kyle more often, and BM won't let him.)

Almost every weekend we have SS3 we try to get together with John so that the boys can play. They've become friends, especially now that SS3 and Kyle have matured more to be able to play games with each other. When we go on walks in our neighborhood, SS3 knows that Kyle lives with his mom in "that" house, but they've never played together on Kyle's mom's time. But SS3 has started asking if Kyle can come over to play, since he knows that Kyle lives so close to us. Or he asks us if we can invite Kyle to the park, or do other things.

Would it be appropriate for us to be friendly with Kyle's BM so that our boys can play together? John loves the idea that the boys can be closer friends. John's pretty sure that his ex would NOT like the fact that we're friends with him. Would it be appropriate for us to knock on the BM's door and mention that we're on our way to the park, and would Kyle like to come with?

AND one more thing to add...Kyle's BM knows SS3's mom but they never get the boys together (that we know of). It seems like it's a relationship (Kyle and SS3) that could be cultivated in both households for BOTH kids...doesn't that seem like a win-win? Or is that just going to create some kind of drama for all of us?