I could talk (well write) about the history of side saddle for hours but I'll try to keep this brief haha!
Originally ladies rode facing completely to the side on a planchette. They had no control of the horse so had to be led by a man, and it wasn't possible to go any faster than a walk.
Then a pommel called the fixed head was added which allowed the ladies to face forwards with their right leg hooked over the pommel, and to ride independently.
In the 1830s a second pommel called the leaping head was added. This sits over the left thigh and gives greater security which means it's possible to gallop and jump. This meant Victorian ladies could ride fast across country with the hunt while still looking elegant.
The two pommels are hidden by the apron / skirt which is why there is the illusion of being balanced somewhat precariously. I've attached a photo from an early lesson which shows how it works!
Eventually I'd love to have a collection of habits from the 1700s through to the 1920s...
The left leg is used as if riding astride and a whip is carried in the right hand and used as if it is the right leg. Most horses adjust to it fairly quickly