Ahh stressful. I don't see that you did anything wrong, nobody did, I imagine R didn't know what she'd be feeling until she was already in the middle of it, and an hour is a short enough time that it hopefully would've gone smoothly for all involved even if she had a few moments of angst. I don't know if you'd been open to J about how important she was to you (I'll guess you have been) and perhaps if R didn't know that, she feared without kissing/hugging in front of J, that she was dismissed as a less important partner (LD would contribute to that for a lot of people).
The only thing I could think of to do in the future if the relationship with R continues, is that you go out of your way to ask her what would make her comfortable if she is present with your other partners in the future, and maybe to suggest a "signal" if she needs a break or minute aside with you. That's not so easy during a short sit down visit, but for parties or events should be very workable.
I like all GG's advice except for I probably wouldn't ever say "J checked in and she thought it was fine" in case R is worried about comparing - "J is fine with everything so they are thinking and discussing that there's some problem with me!" New is stressful, I remember a decade ago totally liking my boyfriends new partner but being overwhelmed with the new social situation without an escape plan in place. As long as R is open to communicating about ways to do it better in the future I'd be optimistic. If R is shut off from finding ways to move past the discomfort, then I'd imagine there won't be much chance of moving past a compartmentalized relationship, which has its own thoughts to think about.
I guess my main worry would be her displacing her upset with HERSELF for not speaking up sooner and her upset with YOU onto R (who it seems behaved decently, politely, and friendly like), and I'd be focused on clearing that up before much else.
Happiness will never come to those who fail to appreciate what they already have.