I agree with Mark H regarding developing good mechanics. I don't think you need to purchase the specialize bat especially if you think it's too heavy for your daughter. Having a heavy bad will make her have a harder time swinging through compared with swinging a bat just right for her.
Make sure to practice her swing everyday even it means just swinging in front of the mirror. Tell her to use her hips as well to help her with finishing through the ball.
To have variety in hitting drills you can thy these out
I have two of the Muhl kickers (each of the weights). I bought them to use in lessons with the pitching machine, looking to add to our warm up drills. I have found limited value at best. I can accomplish the same effect will drills during tee work. My advice would be to save your money.