Is there a graceful way to change skating instructors? Not really. Why? Because most teachers I know give their heart and soul to their students and their lessons. Giving 100% of yourself and then being told that it's not enough (for whatever reason) is disappointing and who can blame them for taking the decision personally? Kind of like a relationship...
I talk to a lot of adult skaters, from beginners to intermediates, about coaches and what each coach has to offer. Although they won't say it outright, I hear them dancing around the subject with phrases such as "maybe try a different perspective" or "think Mary has more of a jumping background" or "I'd like to test and he's not a member of the (insert organization)." It's difficult to change instructors because in all likelihood, you've developed a personal relationship with them, like them as people, admire them as skaters, and all the qualities that make two people friends, with the caveat that you're paying money for their time.
My personal experience has been that I never really change, or drop, coaches I like for any period of time. Each instructor offers different elements of skating that I look for and I go to them to work on certain things. One instructor is incredibly graceful on the ice and I look to her for the form, posture, carriage, and generally how I would like to look on the ice. Another instructor is the "queen of edges" and I look to her for, well, edge work. I work with another instructor on jumps because whenever I would approach a skater whose jumping I particularly liked, they would invariably tell me that they were working with Bob, so I decided to take a few lessons with Bob.
And the one constant has been that I don't hide this from the other instructors. I skate in a rink where everyone knows each other so it would be silly for me to even try. Of course, I don't go out of my way to let them know that I'm working on this element with so-and-so, but as an adult skater, it's easier for me to be diplomatic about it. And let's face it, it's my money and my time.
I remember when I was just starting out and taking private lessons at Sky Rink, my instructor at the time would lay on the guilt trip -- "You can't miss a week, this is my only source of income." Or sometimes engage in unethical behavior -- "Can you pay the cashier and get your lesson ticket but I'm charging $5 extra so can you give me $5 in cash along with the lesson ticket?" At the time, mind you this is 15+ years ago, I didn't mind because I was learning a lot from her and what was the big deal with five extra dollars per week for so much enjoyment? Now, older and wiser, I would know to distance myself if faced with a similar situation. Not that they're bad instructors, but as an adult, I would take into account how they run their business as a whole, which is something I wouldn't have considered as a newbie.
In the end, I've always been a proponent of trying different instructors and not feeling (or made to feel) beholden to one. If an instructor is great, from basic skills to simple jumps to whatever, they will be totally okay with letting you go and allowing you to try different coaches because chances are, you'll come back to them in some capacity. The more you know about skating and have exposure to different teachers, teaching styles and personalities, the more you remember the good ones and the ones that you click with. Bottom line: It's okay to explore.