I'm new to this list & already feel comfortable here after reading a number of posts!
I'm an animal trainer & horsemanship instructor, and (was) a hoofcare practitioner, not currently practicing that because I have 2 little kids & can't do it often enough not to do my back in!
Great idea, to get her skills & communication up with the horse before she rides! If when she's experienced she get's in the habit of still doing a few games before riding, it can be like 'pre-flight checks' to see what the horse is feeling like that day & whether she's ready to ride too, so is a good safety measure.
I would be getting her to teach the mare to yield(move softly with understanding, not escape in fear or resist the pressure) away from various signals & direct contact(finger pressure, rope pressure, whip/stick...), so that she can control where she goes - forward, back, right, left.... if the mare already knows these cues, still good practice for your daughter, to teach her (more)patience and the importance of timing & instant reinforcement. Also teaches her to be expressive and effective with her bodylanguage.
I would be teaching your daughter how to use approach & retreat to desensitise her horse to all sorts of toys & stuff. Another one for timing & patience, but will also teach the horse that she can trust your daughter, even in the face of scaries.
And to put the above into fun practice... obstacles, targetting - get the horse to go and touch or put a foot on whatever you direct her to - driving, in & out the horse trailer, go for walks together.... let your imagination & sense of safety be the only limits!
While I don't follow Parelli, or anyone else particularly - bit of a mix n matcher - I think a lot of what he has is great for beginners & kids, especially his '7 Games' and I can highly recommend it. You could buy the 7 Games DVD, &/or his book, which has all the basics in it, but you should also be able to find the relevant info if you did a google search on it, for free.