I've had too many coaches.
Coaches use and teach many different athletic methods to achieve goals. E.g., you have an incredibly large number of muscles, and you can use different sets of muscles, and different body positions, to achieve similar results. These methods vary from coach to coach. This can confuse you. Unless your coach is unable to meet your needs, it may be worth staying with your current one. Especially if the current coach has a teaching style that fits your learning style. Of course, if your current coach doesn't teach in a way that you learn from easily, or isn't good enough for your skating level, or can't meet your schedule, it may be time to switch.
For me, part of the problem is that I am not a natural athlete. I needed a coach who could do all of the following:
1. Demo the moves well.
2. Explain what to do, in extreme detail - e.g., help me figure out which muscles would create the most efficient way to achieve the desired motion.
3. Explain what I was trying to achieve - in a physics sense. For example, a lot of figure skating involves transferring linear or angular momentum from one body part to another, and/or to the ice. Ideally this involves moving certain muscles to create certain motions, often very subtle motions, but it also involves stabilizing certain joints (e.g., in your core), so the transfer occurs efficiently. A good athlete possibly KNOWS this instinctively, and does not need help achieving it - but I did not.
Few athletes, no matter how great, meet these requirements, because most athletes don't need to think about what they are doing - like the Nike commercial, they don't think, they just do. They can watch someone else do something, and imitate it, without much thought. And they can't explain what they are doing. If you aren't like that, it can be frustrating for both of you.
(Most young kids learn more instinctively than most adults. Analytic and word-oriented learning styles are more typically associated with adults - but I take it to an extreme.)
I also like people with well organized disciplined teaching styles. I like being given practice drills that practice all relevant skating skills in a repetitive, organized manner. That's not for everyone, but it is for me. I find it a very time-efficient way to warm up and practice. I also like to master one skill right before moving on to the next - many coaches teach you to just barely sort-of learn something, then go on, and later go back and correct the incorrectly learned skill several times over. (In fact, all ISI and USFSA group lesson plans encourage that poorly learn, unlearn and re-learn approach.)
A lot of my problems were that I asked an officer of a local club for an entry level ice dance coach recommendation. She gave me the name of a Russian coach with Olympic credentials, that she had worked hard to convince to come into the area to coach, so she was trying to help him find students. Needless to say, he was very expensive. In addition, he was a guy, whereas ice dancers are better off with someone of the opposite sex to partner with; his English wasn't very good, which fit very poorly with my learning style (but worked very well for some of the more athletic skaters); and part of what had made him a successful competitive ice dancer was that his skating and partnering styles were unique and distinctive - which made it difficult for me to partner with other American ice dancers. I also wanted to do some low level freestyle skating, which he didn't teach. On top of that, he mostly coached private lessons at rinks that were a bit far from me, during expensive club sessions of those rinks' clubs, which I had to join. And his other students were competitive level ice dancers, so he could not help me get together with an ice dance partner.
It took me a long time to understand all these issues, so I switched several coaches before I found one who fit my needs better.
None of my coaches had any problem with my taking lessons from other coaches. Maybe that is partly because I wasn't a competitive level skater, so I was no great loss. But it is very polite to ask your coach's permission, before taking a lesson, even a trial lesson, from another coach. If a coach was too insecure to let me try a lesson with another coach, or try to learn some things from the Internet (like this forum, or Youtube videos) I personally would avoid them, and I would ask that question of a coach before trying them out, but I admit a lot of coaches disagree with that opinion.
If you must switch, I suggest you watch other coaches teach a few other students before trying them out. Avoid anyone who is in the least bit abusive or inconsiderate. You shouldn't have to deal with that, and they are also likely to get banned from rinks. Figure out what your learning style is, and see whether they ever use that style, and see whether they have experience teaching someone of your age. Do their students appear to advance in skill during lessons, and find out (e.g., from skating judges or people who run club tests and competitions) whether their students do well in tests (they should almost always pass any test they take) and competitions. Take a group lesson with them if possible first - not only are group lessons with the same coach a good inexpensive supplement to private lessons, but group lessons are very hard to teach - if they can manage that well, they can manage almost anything. If you belong to ISI or USFSA, you may be able to find out what their genuine coaching credentials are from those organizations. As with most things, credentials are largely irrelevant - but to guide you during a test or competition at your level, they may be required to have a certain level of credential and/or rating. And of course ask their other students, especially other adult students (assuming you are an adult), how they feel about them as coaches.
It would be very cool if one of the coaches who writes on this forum happens to teach in your geographic area. Look at their explanations, and see if you understand what they say. Some of the coaches here are extremely good at explaining things. Otherwise, the best you can do, like I indicated, is to come close to where they are teaching, and listen to them teach, and see whether you understand what they are saying. (Do NOT come so close that you interfere with the other person's lesson. Give them plenty of space. And never talk to the coach during another person's lesson.) That is sort of impolite, because it looks like you are trying to get their teaching advice for free, and I'm sure some coaches wouldn't like it at all, but I can't think of a better way to find out if they meet your needs.