The bit you posted is a good one, presuming your horse is already trained to neck-rein and you will be riding one-handed with some slack. I'm guessing that by solid mouthpiece the rules won't allow anything hinged like a Myler or Billy Allen? If so, that doesn't leave yo uwith many options, and what you have is about as good as you can get.
As for the rearing mare, I'm also assuming that you've had her teeth looked at, and that you're asking her to stop first with a seat and vocal command, and then by increasing pressure on the reins--and that she's otherwise well-trained and responsive to the bit. Good luck with finding something suitable for her.