Ok, things are back to stable. What I had felt was a change of rules around C's interactions with my kids, turned out to be more of a misunderstanding. My husband had never meant for C to spend purposeful time around my kids. We discussed all this at length and arrived on a compromise where I can take the kids and do things together with C (even if we have an intimate relationship), as long as I first let my husband know the plan, and make sure it is not an activity he was planning to do with the kids himself or otherwise feels is too sentimentally important (their first experience at something, etc.). But basically, we can do whatever I'd be able to do with any other friend.
The other option was to keep physical intimacy out of my relationship with C, and be able to include him in social events with my husband, invite him to our parties, and otherwise treat him like any other good friend all around. This was really tempting to me, after that one afternoon with both of them together, and after thinking that was the path we would have to take and imagining such possibilities as a trip to his rural home. If we are intimate, my husband will not consider him a friend and I'll have to associate with each of them separately.
Yesterday C and I spent a few hours discussing both options, and had a very hard time making a decision. In the end, we realized that if we chose the no-intimacy option, it would be with the idea that eventually my husband would relent, or maybe we would just falter, and we'd switch back to intimacy. My husband was clear that he didn't want this to be a back and forth decision. So we decided the only sustainable option was to allow the intimacy, and forgo his interactions with my husband. It's bittersweet.
Another interesting piece of our conversation was a discussion about C's evolving views on monogamy. When we began, he was clear that polyamory was not in his nature, and as much as he loves and respects his former partners, he didn't see himself capable of maintaining more than one relationship at once. Wanting a full partner eventually, it was a given that our relationship would end when he found the right woman who could offer what he is looking for. Now, however, even though he is still ostensibly seeking someone who can offer more of herself than I am able, he says that he would only end his relationship with me if the new woman asked him to be monogamous. Of course, this would be the most likely scenario, so he figures he'd be ruling out most possibilities if he limited his choices to someone who'd accept his continued relationship with me. On his part, though, he would be willing to give polyamory a try. This is new, and even though it's unlikely, it comforts me to know that he doesn't foresee changing how he feels about me even if he finds a new love. Perhaps we would just switch back to the "no intimacy" option and keep the love going.
Who knows what the future holds? For now, things are back to where they'd been feeling pretty good. I'm content.