Correct saddleseat should not be giving a chair seat. To post correctly, you need your legs under you, not bouncing up into it.
I knew of several hunter/jumper riders who were taking saddleseat lessons to develop their hands too, as well as balance.
I would keep looking for what you think she would be most interested in, as well as you if you will be most likely to drive too, as too expensive to drive far nowadays weekly. If she expresses an interest in saddleseat, then I would let her try it. If it is Saddlebreds they are using, those are some amazingly people oriented horses, and very talented too.
I would let her try it, as closer to travel to.