Let me throw this thought out. There is a big difference between the desire to do something and being driven to do it. I'll use sports as an example as I've given it some thought. There are many people who fall in love with a particular sport and take part every chance they get. That's desire and if that's all you've got you may be very good at the sport but you won't make it to the Olympics. If you are driven you not only practice the sport in question but you train in other ways. You do weight training, aerobics, ... You not only get a coach for your sport you get other types of coaches, motivators, ... You give up other pleasures. If your sport is seasonal you travel to follow the season.

It works best if the drive comes from within but perhaps it can be imposed parent to child. If it is imposed and not matched eventually by the drive from within it will die eventually. Mozart's father may have pushed the young Mozart along but without the internal drive it would not have lasted. The initial push may be good to encourage the drive from within.

Musically I bet you can separate those with desire from those with drive by looking at who sets aside a specific time and duration to practice. Those who are driven practice without applying a structure. You probably have to drag them away from their instrument(s).