I just want to share my personal experience, and it may or may not strike a cord with you.
My dd (first child) had SERIOUS feeding issues. So much so that she ended up in two feeding programs, saw numerous ped GIs, took many different types of meds, etc. She had silent reflux and sensory issues. We have been working with both since she was a tiny baby.
Anyway, I would have given ANYTHING ANYTHING to have her eat/nurse/drink, etc., like a normal child. She would not. Many children in her situation end up on NG or mic key button feeding tubes. In our case, we learned that if she was asleep, we could slip a bottle into her mouth and she would naturally suck. This meant keeping our house like a tomb, no phones during feedings, no TV (which is no big deal). We would often pray that no one would knock on our door and wake her, etc.
This went on until she was 14 months old. At which time I just couldn't do it anymore--rocking her to sleep to feed her--or putting her in the car and driving for hours to stop somewhere on the side of the road and climb in the backseat and feed her. It was pure insanity.
Anyway, at 14 months, she would only drink water and didn't start drinking milk until she was 18 months old. She still won't TOUCH juice or many many types of foods. It's really tough to worry about her all the time.
The reason I tell you this story is because when my son came along and had a healthy appetite for nursing--I was THRILLED!!! So for me, he can nurse ALL night if he wants to--he is gaining weight and I TOTALLY LOVE being able to take care of his needs. When my dd woke at night, we could only walk the floor with her, because she would refuse to eat (which usually settles most babies).
That experience for me has taken away anyone else's right to tell me when or how or what I should do for my son. It's not that anyone else had that right to begin with--but I did give my power over to others when my dd wouldn't eat. I've already experienced the pain and devastation of listening to doctors tell me what to feed my dd and I was stupid (and inexperienced) and stopped nursing her at 2 1/2 months. I would have preferred to nurse her in her sleep instead of give that up. But I didn't know enough to contact an LC and we went through pediatrician after pediatricion who all shook their heads and said that they had never heard of a child who wouldn't eat.
Now I find that that is a common experience.
I guess what I am saying is this: don't give your power over to this woman. There is something obviously wrong with her (insecure, etc.) and she is using that to wield power over a group where she feels like she is in control.
You don't need to explain to her WHY you want to do what you want to do with your child or HOW or that you feel like you MUST. It is not for her to decide or for her to make a judgment.
If it helps, take a break from the group for a while and then when you return play dumb (if you don't feel like you can actually confront her or talk to her) and say: Guess what? My ds no longer nurses at night! All fixed!
Otherwise, pull her aside and be as gentle as possible and ask that she not use your name during discussions as it makes you feel uncomfortable (kind of like I said above).
Good luck. The problem here is the LLL leader, not your parenting choices.