Her reaction reminds me of how I felt a couple months ago, when my husband took me out for beers with his railroader work buddies. Right before my eyes, my considerate, loving husband transformed into this crass, insensitive macho. He's in his 40s and the guys who work under him are in their 20s. In my eyes, he basically reverted about 20 years.
At one point, he went out for a smoke with one of his coworkers and told me that the other would keep my entertained. I felt pawned off. I'm an introvert and I don't especially care for talking to strangers, especially when I feel no real connection as was the case here. When someone takes me out to meet people, I expect them to keep the conversation gears greased.
It would appear that R struggles to be open with you. My husband does, too. That's why when he finally does work up the courage to say something painful but important, I listen with my rabbit ears pointed straight up. He doesn't make those comments lightly, and dismissing or negating them would be the quickest way to clam him up for good.
Maybe she's being overly sensitive. So what? She's asking you for help and support, and even giving you very specific, unambiguous examples of how she'd like you to behave next time.
When you choose to date a sensitive person, you can't just expect them to suck it up. They'll need a little more support and compassion than some people. Providing that support is the price of admission.
When my husband took me out for beers that night, he felt that the evening was good fun, as did his buddies. THEY were all having a grand old time, hitting on the waitress and making objectifying comments at the table full of women celebrating a birthday beside us. Quite frankly, their opinion on how the evening went is less than irrelevant to me. I was hurt and offended, and that's all that matters to me. A get together can only be considered successful if all the participants enjoyed themselves.
Going forwards, if you insist on them meeting again and being buddy buddy (not sure that's even necessary, btw), you'll have to man up and take on more of the responsibility in how the evening goes. Ask R how you can help support her. At some point in the evening, take her aside privately and ask how things are going and if there's anything you can do to make it better. In a nutshell, listen to her and help her when she asks for it.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker