Would something like this work?
KidCo Mesh Window Guard : Target
I guess there are many varieties of things like this that kind of fit inside the screen to reinforce its strengh and might be easier than building and painting wood ones. Or probably just a bar or two of aluminum criss-crossed and nailed into place or parallel to each other across the bottom 1/3 of the screen would reinforce it enough to rebuff her if she tried to plunge or claw through. Good luck!