Spiritual Faint of Heart

I'm a little confused. I have this new challenge in my prayer life. It started the day of Corey's funeral. Spiritual numbness, maybe. Then, two days ago, Hanna woke up at 4am throwing up. By Sunday morning at 5am, I was pleading with God to please make it stop for her. So pitiful was she. And by 6am, I was claiming His own character as the basis for it, begging Him to show my children how faithful He is to answer prayer. How loving and caring He is to not want any of His children to suffer. I was sure He would listen and make her suffering stop. But 15 minutes later, while again holding the "barf bowl" I found myself to be wrong. So now, as I pray that God would spare Grace (everyone in our family, actually, but especially Grace) from this horrible stomach flu, I waiver in my faith. He said we should ask, believing that we have what we ask for. But how do I do that if He doesn't even answer the prayer that protects His reputation? For His Name's sake. I don't understand! But I know that even in that, God is sovereign. And I so badly want to believe that EVERYthing He does is good. So I guess I'll pray that He helps me in my belief.