Everyone says that the bit doesn’t matter but it honestly does.
I know of horses that genuinely enjoy being ridden in stronger bits. Odd but if they like it . . .
I changed bits and my horse is much happier.
Anyways, I would go to your local tack shop and ask someone there if there’s something with mild leverage.
Any horse can ride in any bit with control. It all goes back to the basics. How is the horse reacting to the bit. Acceptance or disregarding. Do more turning, backing, and transition exercises
People are so quick to say sort your flatwork but coming from experience, some horses generally are little tanks and I know I would rather have soft hands with a strong bit rather than hauling at her mouth cause she’s in a snaffle! Try a Waterford, makes it hard for them to lean on :) and they come with lots of different options ie loose ring, 3 ring, pelham to suit different horses.
In my opinion the bit doesn’t matter. Just ride from your seat and leg and you shouldn’t need a strong bit. Sometimes a full cheek is helpful for a quick correction
Is she accepting the bit or trying to avoid it? Also is she leaning on it or putting her head up to high? It is hard saying what but to advise if all we know is she is too strong! 😊