The bait-and-switch method of adding a second coach could also give the old coach a reason to accept new students to fill your slot. The door swings both ways when you start using intimidation as a motivational technique and it usually backfires. Really bad if the new coach doesn't have the time available, or says so, so as not to get involved with the coach-hopping. Coaches aren't stupid, they're business people.
I had a skater take a lesson with a different coach during the time slot I had saved for her, saying that she would take her lesson with me on another day instead. I wasn't going to wait around for her to update her schedule - I had two other students interested in the time slot she dropped with me, so I filled the slot. Turned out my other available times didn't work out for her schedule. (Not sure if this was intentional, but it was what it was.) Pretty bad when the second (now only) coach decided to drop that day from his/her teaching schedule. The student actually expected me to tell the other student that she couldn't have that lesson slot anymore. All the other coaches were full and she didn't want to come on a different day, so she spent the season practicing without any lessons.
If you want to change coaches, do it. I don't have a problem with a transition/tryout period, but being deceptive isn't really the way to go about it and yes, you can get a "coach hopper" reputation, although that's more common among young skaters with skating parents.
Better to act like an adult and discuss your concerns and plans.
But what happens if the coach doesn't agree with the new coaches technique and advises against hiring the second coach bc they feel it will ruin what they taught you? Its just a thought.
An entirely likely situation.
That's why coaches often "team teach" or "team coach" so that they have 2-3 other coaches with similar styles of teaching and technique. This way, the skater doesn't get mixed messages from lesson to lesson. If you choose someone else, and the primary coach expresses that concern, you should seriously consider your choice.
Take jumps: one coach at our rink teaches beautiful jumps in the same "style" that I do, so I have no qualms about having her jump-coach my skaters. I know that the skater won't have to deal with two different techniques. Another coach whose jump style is radically different would mean re-learning existing skills using the different style/method.
Which style do you use? Do you switch from lesson to lesson? Does the skater choose which method to use? It's a dilemma.