For anyone who comes here looking for freemount help, I’m going to (perhaps pointlessly) comment on some of the earlier posts here. But mounting hasn’t change since 2016, so hopefully there’s some relevance…
I think I also learned freemounting from the Schwinn manual (1979). I don’t remember curb starts being very difficult, but their example for mounting in the open was the rollback mount. That took a while, due to the obvious “rolling back” part. That’s not the best mount to start with in the open, but it does start introducing you to idling and riding backward.
If that’s true for someone leaning today, I would suggest you probably have your seat too low. Try to avoid that, because in the learning stages, the more your legs are bent, the quicker your quads will burn out.
Your kids probably learned freemounting faster for two reasons: 1: They were kids. 2: They got better at riding, perhaps, before worrying too much about the freemount. This made learning the mount easier. But mostly because they were kids. 
Idling is not impossible. You might have some mental baggage getting in your way, but it’s a pretty basic skill. Easier on a smaller wheel; use a 19" or 20" if you have one available. The bottom foot does all the work; all the pushing and all the stopping. You have to pedal a big enough arc to be able to push that pedal the opposite way, and not do it too fast. Meanhile, hold onto a support, as lightly as possible, and work on your side-to-side balance. Combine this with trying to ride backwards. I’m guessing you haven’t learned that. If you have, idling should come very quickly if you focus on it.
I guess it starts out that way. Most people end up doing what I call a “Dead Spot Mount”. This is where one foot is at the bottom. It’s easier to hold the pedal there, but much harder to ride away from that position (which is why it’s called the Dead Spot). People push forward, get their other foot on the top pedal, and can’t go anywhere because they’re only just balanced. They didn’t let themselves rotate a little bit ahead of top dead center. That’s why it’s a lousy way to freemount.
Perhaps that’s why Schwinn recommended a rollback mount in their manual. It breaks the ice on rolling backward (and idling), by instructing you to push the wheel half a rotation to the rear. This puts your other pedal in a position when you can apply power to it, and if you’ve rolled back enough, you have to go! But it’s hard too.
That’s a great way to describe how you do it. It feels sketchy as hell at first, but really, what you’re going for is just to hold your knee joint at that specific angle while you swing up onto the uni. Don’t let it bend in either direction, and you’re golden. This is easier said than done – it gets a lot easier as your legs build up to meet the effort of riding the unicycle.
I can’t remember the time period of my learning to freemount. Probably not very fast. But then again, it took me a very long time to learn to ride. I started in 1976 (I think) on a junky, department store 16" uni with a hard plastic tire. I could ride it a little bit, but then it kind of fell apart. I was unable to keep the wheel from stopping against the fork when I tried to make turns, so that was it for three years. Then my neighbor got a Schwinn Giraffe, and eventually, the rest was history…