It's okay to be sad, but remember that you took her in and gave her the last, best year of her life. For that, you deserve kudoes.
She was loved and cared for, and in the end, that's all that counts.
I'm sorry especially for your daughter, but at least you have the opportunity to teach her that when our non-human friends are suffering, the greatest gift we can give them is peace, and to be pain free.
The best description of a true horseperson is being able to let them go when it's time, even though it will emotionally devastate us. The riding part is immaterial; even a bad person can ride well. A true steward of the animals puts their animal's well being before their own desires.
It seems to me that you're a true steward.
Godspeed, good horse.
Say hello for me to the little bright bay Arabian at the Bridge with the perpetually pinned ears. He's been there almost 2 1/2 years now, and would be glad to show you around.
Leap, prayers of peace for you and your family. What you're doing isn't easy, but it's right.