There are 4 inches in a hand, so 50 inches is 12.2 hands and yes, the mare is 16 hands.
She has the bloodline potential to be a money earner in the cutting arena. The only problem with that is, the training and tune-ups and show costs for cutting horses is expensive...and not really conducive to making kid horses LOL.
Unless you want to be competative in cutting, I would just get a solid base of training on her. Have a trainer that will ride her a million miles on trails, through town, along highways, etc and expose her to anything and everything scary. If you eventually decide you (or someone in your family) wants to get into something like sorting or penning or even cutting in smaller shows, then you can talk to a cutting trainer about putting a little cow training on her.