Well PGM35, I think this woman just has a bug up her butt about something. I think it's a shame she's decided to keep whatever it is secret from you just to spite you. That's what it sounds like she's doing to me.
Have you considered asking one of the other women in the cycling wives what it may be? Someone you are close to & could confide in, who wouldn't blab to Miss Bug-up-Her-Butt that you were aking. Maybe it's some inadvertent slight that she felt or misunderstood, that if you knew about it you could approach her in person & explain or even apologize for the inadvertent slight.
I also knew a woman who was part of our large "wives" group, back when I was married. She was always pleasant to my face whenever we were at someone else's house or any kind of event. But from day 1 of when we met, whenever she invited women to get together for lunches, or parties, even children's events, I & my children were always left off the list. I told myself "maybe she just forgot" "it wasn't intentional". But it happened every time she was the inviter for anything, for over 20 years. Finally it became clear that it was intentional. My name was deliberately left off a Christmas card, when everyone else in my family was listed one by one, by first name.
To this day, I have absolutely no idea what ever caused her to feel this way. There were never any unpleasant words, actions or inferences made by me, to her face or to anyone else.
She passed away a few years ago unexpectedly & to be honest I felt no sadness or regret. I'm glad she's gone so as not to slight me anymore. I didn't waste my time going to the funeral or even sending a card.
Everyone else who knew her went on about what a wonderful woman she was, full of Christian kindness, giving & a joy to be around. That's NOT the woman I knew, but I kept my opinion to myself. I thought: "yeah, right, some Christian kindness she had."
Some women are just like that. They seem to feel treating another poorly gives them power. They pick a victim & that's just the way it goes. No one wants to rock the boat & be the new victim, so they don't bring it up.
I think maybe your "friend' may be one of these people. If you want to try to have a friendship with this woman, I'd suggest you try to find out what's wrong quietly & then clear the air with her. If that doesn't work, quit feeding her ego. Don't go out of your way to jump through hoops for this woman. You'll never jump high enough.