Pftt. Patting is probably more for the benefit of the rider than the horse, but as smrobs said, they will pick up the intention behind it, so pat away; and tell the bully to mind her own business people like that are a pain in the backside.
I'm a lot like you, where I don't want to really hurt someone's feelings and am so tolerant that I have to force myself to put my foot down, before things get out of hand. You can always practice what you want to say, and recite it before you say it- like writing an essay, you can revise until you're satisfied with it. But eventually, if you keep playing along, she's going to notice that you're not doing what she's saying you should, and you will be put in a tight spot when she asks why- it's just putting off the inevitable. There will be more hurt feelings the longer you put this off- think of her like a hot air balloon. You're just helping to fill her with more and more hot air, and you can either stop it now and just let things deflate or keep going until she eventually explodes.
Soenjer55 is right. The problem is too many of us are nice and it can sometimes be hard to just say “no” or “I’m not interested” because we are afraid of hurting someone else’s feelings or something. My girlfriend had recently had that trouble. Her friends were always wanting her to go and do things with them, shopping, going out to dinner, nothing nasty, nice things actually, but they were getting in the way of her work and it was putting her under a lot of stress. I had to convince her it was OK for her to say, “no, I’m busy”. She did eventually say it; her friends were a bit miffed for a day or so, and now they just get that she has to get through her work. And my girlfriend is much happier. My guess is that if you just say to this person something like, “I appreciate that you are just trying to help, but I really need to do this on my own; but I would also appreciate it if I could come to you for advice some time” she might back off and give you some space and probably not get her panties in much of a bunch about it. Let it keep going and it will probably just get worse.
Tell her that if she wants to be a trainer, you'll pay her to shut the h*ll up. When people do that to me, I just completely ignore them and do exactly what I'm doing like they're not even there... that usually gets the point across.
I personally don't like to pat horses just because it can make a sound that will make some horses uncomfortable, if I show affection to a horse I will usually just scratch because horses seem to like it more than petting. You can teach a horse that a pat is good though, and it's a lot easier when you're riding to reach down and give your horse quick pat than to scratch.