I'll be honest, my daughter isn't a natural athlete, but she works hard and she is improving and advancing (obviously), just not as quickly as her friends. I've tried to tell her that she's doing great, and I've even shown her video of her progression over the years, but it doesn't seem to make much of an impact.
Does anyone have any advice for how to get her to focus on her progress and her skills, and to not worry about what everyone else is doing on the ice?
You've just described my own daughter, except that I am a skater myself (I even teach classes) and my daughter has been skating for 3 1/2 years, and only just passed into FS1. My daughter is
extremely self-critical, which I feel has limited her progress more than anything else, she honestly has the physical ability, but she's easily discouraged because she's so critical of herself, so it's extra difficult to get her to spend the time practicing something she's struggling with.
My daughter has competed once, in compulsory moves, and while she did well enough, she has zero desire to do it again (which is fine - she met my goal of trying it, and she spent the next two months showing off the medal she won) - but she LOVES participating in shows (as part of a group) and other group performances that our rink does though... I think it's because there's less focus on just her individually, so she can't do that destructive overly critical thing to herself, she has to focus on the group and she knows she has to skate as part of that group.
That said though, I really don't view my own daughter's slow progress as a failure in any way - if anything, she's actually benefitting form her slow progress, by getting MUCH more instruction and practice time and truly mastering skills before being able to move up to the next level - the kids who breeze through often spend time later on re-learning skills they didn't actually master/understand, but could do "well enough" to pass through a level - and that only gets you so far in the long run. She's seen friends breeze through, and others who have gotten "stuck" at similar levels to her for what seems like a very long time - so she learned the lesson early that everyone progresses at different rates, and it's okay if you need more time at a level, and we haven't had any meltdowns about "not passing" for quite a long time now - and when she hasn't been moved up, she'll tell me what she still needs to work on before I even ask.
I also have to second neverdull's advice - kids almost always don't do well with instruction from parents - this is particularly hard for me, and when I spend time working with my daughter on the ice, my emphasis is only on encouraging her to practice the things she doesn't like to work on, but I don't usually give any feedback at all on how she's doing - because she really doesn't want to hear that from me, and I, as a parent, really only want to see that she is practicing the things she tries to avoid, so I don't need to tell her anything I'm seeing wrong (unless it's just very wrong, or she can't remember how something goes, then I'll remind her, but that's a little different - it's more just redirection than criticism).
BTW, I also wanted to add for those who think that overly critical kids somehow got that way because of their parents - I don't believe this to be true at all. My daughter has always been highly critical of herself, and I've never done anything to encourage or cause that - it's just how she is. She begged and begged to take gymnastics when she was about 5 (her brother was doing gymnastics back then, and had been on the boy's team at our gym for a couple of years, so the gym was a fairly comfortable/familiar place for her) so I let her. She excelled in the tot class she started in, which was all just fun and games, and she LOVED it, but when she turned 6 and had to move into the "big kids" gym, it all fell apart for her, and very quickly. She was doing okay, but hated the beam and the bars, and while she did try, I could tell it was a real struggle for her - based both on fear and the feeling she had that she wasn't doing as well as her peers (and she wasn't, but SHE was the only one being hard on herself about that, her coaches were awesome with encouraging her, there wasn't any peer pressure or bullying, and nothing bad or scary ever happened to her). Then when time came for the first "competition" (which was really just an in-house competition to introduce the kids to the competition format and what to expect when they did get to higher levels) she completely broke down and started talking about quitting. Even the gym owner was baffled by this, because everything they do to introduce this to the kids is VERY positive, there's zero emphasis on "winning" - the only emphasis is on learning the routines, which are very simple in level 1, and general things about how to wait for your turn, not being a distraction to other competitors, etc. For about a month, every practice ended with her in tears because she was so stressed out about competing, and ultimately I did let her quit, because it was clear she was miserable - and that was all from the pressure she put on HERSELF. To be honest I am sure she could have just chosen not to compete and that would have been fine (and I would have been just fine with that, too) but it was very much all-or-nothing in her mind, and she knew that she'd lose and she just didn't want to have any part of it. She even told me she felt like it was too much pressure and THAT is why she wanted to quit. I'd ask her where she felt that pressure came from because I knew it wasn't from me or her coaches, and I'd just get an "I don't know" from her - it was very frustrating for both of us.
After that experience, when she started asking if she could learn to skate just a few months later I was VERY skeptical... because I really didn't want a repeat of the almost self-destructive pattern I had seen before. Thankfully, while she has made very slow progress, she genuinely seems to love skating (which is something that has grown with her - she was definitely NOT there yet when she started), so that alone has been enough to keep her going. When she first started, my main goal was just so that she could skate well enough during public that I didn't have to be right there with her the whole time if I wanted to go skate - she did manage that within a few months, and I told her at that point that she could quit at any time if she wanted to, but she has stuck with it, despite the fact that she has repeated every level (including Basic 1) several times. I've stayed mostly hands-off with her skating, and I don't coach her (well, I did as she prepared for her one and only competition, but that was not coaching as much as just teaching her the routine she needed to skate - we didn't work on any skills) - my biggest involvement is when she gets new skates, we go through the skills she likes and what she's working on so I make sure she has no obvious blade alignment issues, but that isn't coaching as much as a "let me see you do ____" and asking "do you feel like you're falling on an inside edge, or fighting your skate" over and over.
She got sent home from school with a rash today and her FIRST concern was "can I still skate tomorrow" - so I think she's still excited to go skate, which is good
To be honest I never expected that she'd still be skating now when she first started.