There's lots of anxiety and advice about switching coaches, but changing rinks is another issue that comes up, both for kids in group classes and with private lessons.
Sociologist Ray Oldenburg first proposed the theory of the "third place," those public gathering places, outside home (your "first" place) and work or school (your "second" place), as crucial to healthy civic society. Places of worship are the most common third place, but in consumerist America, the marketers quickly latched onto this concept and started promoting malls, coffee shops and other places of commerce using this idea. The public sphere has been slower to catch on, but parks, community centers, and yes, ice rinks, are natural "third places" because of the amount of time people spend there.
It's hard to change your third place. It's a community, nearly a home, and it's a place whose culture you understand. Anyone who has switched rinks understands how out of place you feel at the new one; how they don't seem to do anything right, and how they don't embrace newcomers. A "third place" that gets it will have programs that quickly incorporate newbies into the culture, be it food in the lobby or multiple extracurricular activities and strong volunteer programs.
So why do it? Well, there are good reasons and bad reasons. Here's some good reasons:
You've moved to a new community
In a new community, choose your rink by proximity, unless you have a reason to go somewhere else, like your old coach has hooked you up with a new coach in the new place, or there is a particularly strong program at a farther rink. No sense adding the anxiety of travel time when you're already anxious about the new place, plus your skater is more likely to encounter kids from his or her own "second" place, namely school, at a neighborhood rink.
Problems with your existing rink have become intolerable
It happens. Practice ice is poorly managed, costs are too high, classes are inadequate or nonexistent, coaches are unprofessional, there's a toxic synchro team, you name it. Start by asking your coach if there's a different place to skate. Most coaches teach at more than one rink. If you really can't stay at your current rink and it's the one closest to you, you'll have to eat the travel time. If you don't have a coach, try signing up for lessons at a different program just to try it out. Ask the skating director at the new program to test your skater so you get placed in the correct level. There is wide variation of passing standards from program to program.
Your skater is specializing in an area not offered at the current rink
This is common with Synchro, Pairs and Ice Dance. You can still take classes at the old rink, but your training is going to happen somewhere else. My daughter went through this, and she missed the people at the old rink, but developed new relationships at the dance sessions.
Your coach changes rinks
This is actually only a reason to move your lessons, not your practice or your classes. You don't have to follow the coach to a new rink. I've seen coaches try this, and the parents all just quit on them, and stay put, because for most skaters it's not about the coach, it's about the family at the rink.
Some bad reasons:
They won't advance my skater, so I'll just sign up for the next level at a different rink. Who will know?
The coaches will out you at the first class, and furthermore they'll start thinking that the people at the other rink are idiots, or why would they have passed this skater?
I've antagonized everyone at the old rink, and am slinking away in shame
Don't do it. Mend your fences, change your ways, and stay put. Every town needs a village curmudgeon.