Also, no leaping head in the period Heyer rides about.

Sidesaddles are very flat, and you hook your leg around the fixed head. You also need longer reins as you're much higher up. It's actually a very secure seat - so secure that pre-quick release stirrups, your biggest danger was not being able to abandon ship. Most riders carry a cane to give aids on the offside, with your leg on the near side providing them there.

However, most impulsion comes from your right leg, which is stretched along the saddle and also along the horse's spine. Again, as with astride, your upper body is far more important than your legs.

There was a big surge in side-saddle sales post WWI, with saddles being made with the horns on the offside, as it meant amputees could ride and hunt again. In that case, the whole leg hooked over the fixed horn, as that's the leg that gives control.

Grip can only keep you on a horse so long - balance is far more
Important. However, it's easier to keep on a bucking horse sidesaddle (use the leaping head) than it is astride.