Get a tax stronger bit and when your horse leans, don't pull but squeeze on the reins a bit.
Pull let go pull let go is good if she is heavy on the bridle
My riding teacher tought me that if you move your shoulders whichever way you want to go, it will move your horse in that direction so you won't even need your reins.
Raise your hands a little bit and release as soon as she gives. <3
I dont know if this will work for your pony but my horse does that same thing and I've been working on using less rein and use a very light contact on the bit and more seat and leg aids. Also getting his hindend and back more engaged to make him carry himself properly.