Does God will that we should suffer?

The Catholic Church teaches that God either wills or allows everything that happens in the world. Even our own personal suffering. I've often thought God has allowed me to suffer through something in order to strengthen my faith or patience or perseverance. And just as Jesus cried out to God three times for his cup of suffering to pass, He also gave up his own will for that of the Father. Is this the lesson then? For us to cry out to God for help, for mercy, for relief and yet to trust enough that we should give up our own will for the will of God. Especially as a mom, I look to Mary as my example - let it be done to me according to Your Word.

What are your thoughts on God allowing suffering? or even His willing that we should suffer? I know suffering in itself may be the result of our sinfulness and fallen state but if suffering leads to such awesome redemption, grace and mercy and we can surely believe that God is the source of all good that comes from suffering, what stops us from concluding that God must have his hand, so to speak, in knowing what we need to suffer or see in the world as suffering in order to act, to grow and eventually to spend eternity with Him in Heaven?