Okay so problem #1: cutting corners
So what do you do to solve this? You already know the problem that's good.
Do you let her cut corners without trying to correct it? Do you try and then give up. This system won't be pretty but the results will be. When a horse arches out from the corner it means there is a habit or a routine going on. Do you dismount a lot in the center. Or do people ride a lot to the inside of the rail. Or do you halt a lot in the middle. Either of these she is doing what she is trained to do. So try getting off in different and completely random spots, if stopping to let somebody do a course exit the arena or wait in a corner that isn't being used. Does she do this at all gaits or just certain ones? If its all gaits then start out a walk and build from there.
Make sure that you are asking her to get into that corner. My horse will do a perfect dressage corner if I ask him but if I don't and just ride then he will cut. They know its easier and closer to the center where most riders dismount
Walk into the corner use and over use that inside leg squeeze bump quick all the above, just get her in that corner if she arches away from it then turn her to the outside and circle around so that she is forced to go in that corner. When she does halt her and relax then pet her and tell her good girl. Walk her out of it ON YOUR SIGNAL!!!! And walk one full time around and try again. Then add corners go every other and and then 3 and so on. Until she is solid at a walk then build to a trot.
Problem #2: Cantering
My system Ask, Tell, Demand. Ask your horse quietly with a squeeze and a kiss or cluck
Tell: tell them with a bump with the lower leg. Every other bump increase the pressure and directness of the bump each time
Demand: get a crop. That's all even carrying it will mostly turn the halo on without using it.
When you get her cantering every stride or every other stride give her a firm bump. You also say she gets to excited after cantering if you keep her on the bit and in control then you probably won't have this problem as much. My horse gets excited but all he does is prance and I much more leg responsive. Which is what your horse probably does. Practice keeping your leg off of her and using more of your seat. Also practice using different leg pressure
Keep her slow while cantering but yes I also said give her firm bumps every now and then. I call this go with legs steady with hands. You tell the horse to go faster with the leg pressure but you bring the horses butt up under them and brings their head in if you let your hands loose a little and let them bump her nose with each stride. Also give and take or seesaw with your hands just massage her mouth with the bit. Also sit on your butt a little more and roll with you hips don't just sit ram rod straight and stiff. Press those heels down and loosen your lower back kinda like you're dancing.
So yea if you want more advice I got lots more and I stopped because I realized this is really long. Haha ask anybody you can't get me to shut up especially with helping people's riding. But good luck with everything!!!
Hardest Thing About Riding Is the Ground!