I haven't heard her trainer mention "half seat" at all. She's told to be in 2point, but also to sit up straight. Is this the half-seat?
It doesn't sound like it. It's kind of hard to explain, but to me it's like the middle ground between a regular seat and two-point. I also bring my butt off the saddle and keep contact with my saddle only lightly.
Here's a quote from Yahoo answers which I think explains it nicely:
In a half-seat position, the rider's seat bones are lifted out of the saddle, and only her pelvis has contact. It is used for jumping when some seat aid may be necessary, especially for sharp turns, when riding downhills, on the approach to potentially spooky fences, or when the rider wishes to collect the stride. This seat is a compromise, allowing the jumping rider to have greater control than when he rides in two-point, but still allowing him to keep the majority of weight off the horse's back.
Half-seat is often seen in hunt seat, show jumping, fox hunting, eventing (jumping phases), and at times in dressage for training purposes, to help lighten the horse's back.
Is the posting sruggle when she is circling before getting the horse to canter? She told me she struggles there, with the need to transition to canter, and get into the 2-pt.
Personally, I did see it there. I don't know if her instructor has been telling her/reminding her but you're supposed to sit the trot in order to canter. This is also helpful (at least for me) for keeping the horse at a nice trot speed for a trot-canter transition. So she should sit, cue, and then
go into two-point- it's not all at once.
Personally I thought she'd be doing walk trot canter for much longer before jumping (from my non-horsey mom perspective ) . It seems she just learned to canter so recently. I don't want to second guess the trainer, but I guess I'd like to try to ask her what are the benefits (if any) of jumping earlier rather than later?
Many people have a lot of expectations a rider has to meet before they can canter or jump. Jumping in particular can be hard and potentially dangerous for a rider who's unprepared.
However, I did go over a few jumps before I should have even seen a cross-rail. I feel that while it's often better to approach jumping later, there are a few benefits. In my opinion, it can increase confidence in your riding, and help spice up your routine.
How are her legs supposed to be? She was told to really relax them and to let them dangle. Is this a valid strategy or is this not done?
Stable, strong legs, especially in jumping are very important. You want them to pretty much look still. However, tense legs are not good. You also don't want to start a habit of someone gripping the saddle with their knees, an easy mistake to make when you are otherwise tense. This may just be a tactic for now, but this is why I said I'd have her be doing exercises to help strengthen those legs.
Watching your latest videos now. Here are some of my observations:
*Elbows should be back. They are straight now.
*She seems to be gripping with her knees to me (it was a fault of mine for a while). A tell-tale sign is the way her lower leg swings back while her knee remains in contact with the saddle.
*Her heels should be down.
*I would like to see a subtler post and again, bring those elbows back and have her lean back and relax.
*Her two-point needs a lot of work. She doesn't seem to be solid at it yet.
I think she needs more work on the basics, but continuing to jump cross-rails and tiny verticals could be beneficial for her. Nothing bigger than 1'5" at this point at a stretch, I would say.
Honestly, and sorry if this contradicts what else I've said as I haven't really thought about it until now. But in almost all cases, I prefer a very strong w/t before a canter, and then a solid canter before starting with small cross-rails with maybe a small vertical thrown in. The problem is that you really can't jump effectively until you have the basics down. At this point, I don't think she's solid enough in general to be doing a ton of jumping. Some? Yes!
These two videos are a typical lesson for her, the way it is split into flat work and jumping. Most trainers wouldn't do it this way, and would just do flatting at this stage? How potentially detrimental can this be for her?
My instructor splits up a lesson into flat work and jumping for my group, and in my experience it works quite well. However, at this stage, I'd feel most trainers would stick to just flatting. Maybe you should talk to her instructor and ask for her reasoning. Just say something like, "I was wondering why my daughter is jumping so early?"
Good luck and I hope I helped!