Do not look forward to the changes and chances of this life in fear; rather look to them with hope that, as they arise, God, whose you are, will deliver you out of them ... the same everlasting God who cares for you today, will take care of you tomorrow, and every day, either by shielding you from suffering, or by giving you strength to bear it. Be at peace, then, and put aside all anxious thoughts.
I don't think I've ever met anyone who has achieved this advice from Francis de Sales. But it is a goal for me, like it is for many who love people with mental illness.
First, falling apart under a burden of worrying and anxiety will not help your loved one. Your stability is a bedrock for them, and you need to try to keep yourself at peace as best you can.
So how? Only with God's grace is any of this possible. The best way to open myself up to that grace is to realize that I need to ask for forgiveness for the sin of worry ... yes, it actually is a sin ... and ask for grace. I certainly can't do it by myself.
I was listening to a sermon from Tim Keller of Redeemer Presbyterian Church, a great church in New York. He pointed out that worry actually comes out of pride and even arrogance. We think we know what SHOULD be happening and are distraught that it's not. So we worry.
Has God allowed something to get past Him? No. God is sovereign, and He can make even the suffering that comes from the illness ... and ultimately from the fallen world ... and make good come out of it for those who love Him. If we repent and reach out for grace, step by step the peace will come.