You have to be careful not to make your wall to stiff, you want it to flex but not give. Reinforce it to much and your mare might as well be kicking a concrete wall and get injured. Have you considered hanging stall mats on the wall? Those will cushion the blow and prevent her from going through the wall.
Personally I wont have that type of horse on my property and would sell her but that's me. Dad taught me with cows to cull out the obnoxious, difficult and ones that refuse to stay in the fence line for a more harmonious herd. The theory works well with horses too.