Your skater is not progressing commensurate with other skaters of the same age, ability and commitment. In particular, she's been working on her first double for nearly 2 years, with no progress for half that time. She's taking 2 half-hour weekly lessons and practicing on her own an additional two hours.What's going on?
Issues with current coach: Does the coach have other students who have mastered this skill? Is the coach actively engaged with the skater during the lesson? Has the coach talked to you about the issue, and addressed your concerns? If the answer to the first question is no, either you're the first (so give her a chance), or you need to switch. If the answer to the second question is no, you need talk to the coach yesterday and find out what's going on. If the answer to all three questions is no, you're probably looking at a coaching change. Caveat: "addressed our concerns" is not the same thing as "won't let parents make decisions/judgments about technique."
Skater issues: Is the skater responsive and engaged with the coach? Does she appear to be working on actively fixing the problem skill or technique or is she just practicing the mistake, (a very common issue, especially with scary things like jumps). Is there a non-skating issue such as stress at school (either good/academic expectations or bad/social problems or mixed/social pressures), family difficulties, growth or weight gain, etc.
Someone needs to fix her double salchow: I think you can focus in on specific skills at a Basic Skills level-- fix her crossovers, fix his 3 turns-- but if the problem is doubles, then there are deeper issues than "can't do double salchow," starting with poor basic skills. Talented skaters who have difficulty with higher level skills almost always have underlying technical problems. Might be psychological (rare, but parents always think this), might be coaching incompetence (rare, but parents always think this, yet oddly don't act on it), but more likely it's problems with basic skating. In other words, you cannot demand that a coach fix one problem when you, as a layperson, can't really know exactly what the problem is.
Is this actually slow for this skater?
Look back at her skating background. If she's made slow but steady progress, two years on a double might not be out of line. If she's "suddenly" gotten complex skills in the past, this may happen again-- it looks like one day it was just there, but maybe all the slogging just finally fell into place. Again, make sure she's practicing the problem skill and not only doing it in lessons. I can tell you that a skater who will not practice a specific skill outside of lessons is going to get the same lesson over and over because she's not making the technique her own. You might need to add some practice time to allow her to feel she's getting everything in.
We've already decided to switch: Then please stop complaining about the coach and just do it. When you do it, do NOT claim that it's because the coach couldn't teach her way out of a paper bag, or start questioning her credentials (e.g. "well, supposedly she had skaters at Nationals, but that was 15 years ago. How come she hasn't had one lately?"), or complaining in any way about her. Coaching issues are, frankly, less often problems with competence than with skater/coach compatibility, which is no one's fault. Complaining about a coach is harmful to her career. Unless you actually want to negatively affect a coach's career, the reason for switching is "it wasn't working out." If you actually think this coach shouldn't be teaching, then file a complaint with the rink, club, or police and be ready to back it up with justifiable accusations.