I think her dd has taken a break from gymnastics already for financial reasons.
I would check the cheer gym out, see what their tumbling instructors are like. There will almost certainly be a spring floor if it is a gym that fields competitive teams, most likely tumble track and/or tramps or air floor. This is standard equipment for a decent all star cheer gym today, it won't be tumbling on grass. I am actually coaching cheer currently as one of my jobs (coaching gymnastics as well). The director of the gymnastics side of the program has a fabulous gymnastics background and is a great spotter and knows technique. With a program like that the only difference is going to be the emphasis on skill groups, for example all 1/2 twisting, front twisting, and most FHS layout combination type tumbling is de-emphasized, whereas comparitively in gymnastics these are important skills we tend to develop at certain levels.
There is some truth in that a lot of it seems to be "chucking" but a lot of cheer tumbling coaches do know how to a coach, it's a question of the various prep levels of the athletes that you have to work with and where you have to get. When you have a kid with good basics who started young and has time to work up to upper level skills along the lines of the trajectory we've created in gymnastics, most of these coaches have the ability to develop skills with decent technique. As all star cheer has become a growing phenomenon and programs are "growing" kids from a younger age, I predict we're going to see a real rise in the overall quality of the acrobatic elements of cheerleading. There are certainly cheerleaders out there who can do some very impressive things.