The OP reminds me of my favorite workplace/management blog,
Ask a Manager, where the blogger answers reader questions about job searching, workplace issues and management, and so many of the questions are ultimately about the fact that people don't like to have awkward conversations.
I'm pretty conflict-averse too, so I totally get it, but you really just need to man up and describe matter-of-factly what you want and what you don't want. If you don't think this woman is doing a good job cutting your hair, state that directly and ask for someone else. Don't reward a unsatisfactory job, don't stalk the place to make sure she's not there when you walk in, etc.
It's funny because, while I don't seek out conflicts at all, I don't mind speaking up if something isn't right. At the same time, it also depends on how much it matters.
The first time she did it, I did say "well, it's a shorter than I was expecting" which is how she knew it wasn't what I was looking for. But, that was all that needed to be said at the time and it wasn't like I'm not going to tip her just because it went shorter.
This last one, when it was done, I did speak up and tell her it wasn't right and that I'd like it shorter. I explained I was looking for it to be faded and blended. It's a 1 guard near the top, down to 1/2 guard, down to nothing. Every other stylist that's done it knows exactly what that is, what to do, and gets it right. So she basically cut the bottom part shorter and didn't do anything in the middle to blend it in. So, I have 2 zones of hair length. At that point, I wasn't going to keep trying to explain to her what I'm looking for. She just isn't getting it. She's the only stylist in there at that time and there's 3 people waiting. So I said that's fine and left. Again, I'm not going to not tip her.
After getting home and looking at it, it was worse than I thought. So, at that point I wanted to get it touched up to fix it. But I don't want to ask someone else to do it while she's there. I should be able to and I get that, but it's just not worth it for being awkward. I'd rather just get it done when she's not there.
So, I'm just going to go to another one and get it done. And I don't care about going back if she's there in the future and just asking for someone else. That part doesn't bother me. I just didn't want to get her haircut fixed by someone else while she's there. It got especially weird when I talked to the manager a couple days ago without realizing she was there as I thought the store was closed and it was just the manager.
It would be different if it was someone I was forced to deal with in the future. I would find a new way to communicate what I'm looking for, etc. Or if she did this on purpose. But, it's really just not that important and I can avoid getting it cut by her pretty easily moving forward. Just not worth making her feel weird about it.