So how do you motivate skaters, especially beginners who aren't yet as invested emotionally, or don't have as much cool stuff that they can do?
Sometimes the issue isn't skating, it's everything around it. You want to watch tv. You have homework. "None of my friends skate; they think it's weird." And on and on.
So this is not always a skating issue, sometimes it's a parenting issue. And the parenting issue here is, who is in charge? They're kids! Yes, they have a strong will, but honestly folks, if you can't get your 5 year old to do what you say, or if you're offering him the option to negotiate, skating lessons are the least of your worries.
In other words, stop negotiating, and just go.
They don't always have to have a lesson
The mom in question was having 2 lessons and and 2 classes per week, at Basic 6 and Basic 8 levels. That's quite a lot of skating at that level; I think she could probably sacrifice one of those sessions to a "fun skate." Take them to one of the weekend public skates, and promise you won't make them "work". At that level, everything they do on the ice is "on task" pretty much, whether they know it or not. Saturday and Sunday afternoon free skates are FULL of kids from the classes; they'll find people they know and make friends and then skating will be about fun instead of about work. (It's also cheaper, plus if they get into it, there are carpooling possibilities, saving you a chore)
If your skaters are doing privates, class, and practice (and maybe off-ice or dance as well), think about "bundling" them-- back to back class+lesson, or tack skating onto an existing trip (piano lesson, regular grocery shopping, immediately after school, whatever) so that you're already out anyway. Some parents do homework at the rink--you get there right after school, get them a snack from concession and do homework, then have skating class as a reward for getting some homework done!
Encourage your kids to develop rink-based friendships. If they seem to connect with a certain child, find the parent and set up play dates, or see if they're at the rink early so the kids can hang out. Sign up for class together; even share a semi-private lesson (this also helps with costs).
What not to do
No bribes. No trades. If you really want your child to skate, and you know she likes it/is good at it, stop making it a choice. You don't have to be mean about it, just matter of fact. Skating is one of the things you do.
What strategies have you used to motivate your skater?