Part of why it looks awkward to you might be due to the fact that she was posting on the wrong diagonal for the first few seconds (she switched when she was right in front of the camera). The other thing is that it looks like she's working hard to post...which she has to. I can tell you, it's hard to post on a western jog and make it look easy because the jog is slow and smooth enough that there isn't enough momentum carrying up from the horse to pop you out of the saddle like it does on a big moving horse or at a long trot. Therefore, all the pop to come up out of the saddle has to come from her and her own muscles.
It takes a lot more work on the human's part to post a jog than it does to sit it.
As for having her sit up, IMHO, it's never too early to start working on correcting that. If you can get her to start thinking about it now, before it becomes a habit, then it will be easier to overcome.
It makes sense about working harder on a smooth trot.