BTW, one thing to consider is to check whether a coach whose teaching methods you like has a short (e.g., 15 minute) gap between lessons or at the beginning or end of a session. They might be willing to teach you then, because it is hard to find other students who want that. Likewise, at some rinks, you can take a lesson while the Zamboni is surfacing the ice, by carefully avoiding it. That too might be a hard time for a coach to fill. With such hard to fill times, you might even be able to convince them to take you every other week, or something like that. I've also heard of students who desire occaisional lessons getting on a coach's list of students to call if someone cancels a lesson.
my current rink doesn't offer separate classes for adults (beyond basic 1-6) so I would either have to take private lessons (which as you know cost more) or be in a class with little kids. I think I would feel a bit awkward being the only adult in the class!
For the most part, adult classes span a greater range of skill levels, which makes it hard to learn much, unless you have a coach who is extremely good at teaching group lessons - very unusual. Of course if there are about 3 or fewer students in the class, the coach can take turns teaching each student - which sort of works - but it is a lot like taking a very short lesson.
Though, when teaching to kids, coaches usually assume a short attention span, and spend very little time on the same skill. They also tend to do more demos than to use words and analysis to teach, which might or might not work for you. After all, you can find demos on Youtube.
But maybe you should get over not wanting to learn with kids. As long as don't join a formal competition against very young kids, it's not that bad, and you shouldn't feel uncomfortable. In a formal competition, you would have an advantage over the youngest kids, who are still having trouble with basic coordination, or have little leg strength, which some parents might view as unfair. Once you are past that age, the athletic kids will probably learn faster than you (unless you have something like a formal dance background, which trained you to learn very quickly), but you might be able to keep up with the least athletic ones.