I've ridden sidesaddle quite a bit, and it IS pretty uncomfortable, compared to riding astride. You feel a bit like you're on a perch on top of the horse, because sidesaddles sit quite a bit higher than cross saddles and there's no way to have contact with the horse.
There are 2 curved, padded brackets protruding on the left side of the saddle: one curving up to hook your right leg over, and one curving down to put your left leg under, and one stirrup for your left foot. You can grip your right leg quite well around the upper bracket. It's pretty hard to fall off: if something really bad happens, the horse and you both fall. Many women got internal injuries from having the upper bracket jammed into their abdomen.
Trotting is very uncomfortable, bumpy if you don't "post" (rise up & down with the strides), but it's hard to "post" sidesaddle because the leg brackets hold you down. Ladies' sidesaddle horses were picked for their smooth gaits. Cantering & galloping is not bad. Jumping fences is pretty awful, kind of a minor whiplash jerk.
Let me know if there are any other questions.
TATYANA