OP, as someone who owns several instruments, has left and come back to them from time to time, and whose son is now beginning one, I'd really like to know about this instrument that you purchased. If it is one that will hold value (a Steinway, or a mid-to-high level string instrument) then there is no reason for any cognitive dissonance. Take good care of the instrument. Your daughter may well pick it up again, if not, it's an asset that can be exchanged for cash should you need it.

My daughter is just your average piano player. I was disappointed when she said she didn't want to take piano anymore after 3 years of lessons. Her teacher said some kids give it up only to come back later. Well, it's been about 3 years, and lo and behold, guess who wants to take piano again!

With a child who has a great deal of talent, I'd say hold on to it for awhile, don't push her, and see if she comes back to wanting to play one day. And if not, sell it, and I'm sure you'll make at least half of the value back. Don't beat yourself up about it. We've all made mistakes. I always tell myself, "I made the best decision I could with the information I had at the time."