To be honest, you can't. Certain traits can be passed on, but it's not guaranteed. If you know that both of these horses are calm, easy to train and excel at a certain event, then you can look for offspring of them with the hopes that the same will hold true.
But you're better off in the long run, in my opinion, to find a horse that's already been started for your daughter. Ground work takes a long time; will she still be wanting to do this in three more years?
What a lot of folks overlook is that even though they've poured a year into ground work, their horse's aren't really ready to ride until sometime between two and three. And then it'll be another year or two for the growth plates to become solid enough for any real strenuous work (which gaming is.)
So let's break it down like this:
A full year of ground work before saddling.
Sometime between 2 1/2 and 3, mounting and walking or light trotting.
3 1/2 to 4, light riding, loping, pattern imprinting
4-5, growth plates ready for more strenuous, serious work and competition.
You may have already know all that, but it always bears repeating