Yes, some people do seem to be natural worriers, constantly pessimistic about the future, just as other people seem to be naturally cheery and optimistic (even to the point of ignoring real problems).
But God doesn't call us to be either pessimistic or optimistic all the time because either attitude ends up ignoring the way things often are. Instead, God calls us to be realistic -- to look beneath the surface and see life as it really is. Sometimes that will make us optimistic; sometimes it will make us pessimistic, but the goal is to see life the way God sees it, and turn to Him for the help and hope we need.
I often think of Moses in this regard. When God called Moses to lead the ancient Israelites out of slavery, he said he couldn't do it and came up with every excuse imaginable. But God rebuked him for his pessimism, and promised Moses that He would be with him and help him. (You can read his excuses and God's replies in Exodus 3 and 4.) The same is true with us.
Pray for your sister-in-law, that she will learn to look beyond her fears and put her faith and trust in God. Then encourage her -- both by your words and your example -- to meet the future with prayer and with faith in Christ, who is the Lord of the future. We can trust God's promise: Nothing "will be able to separate us from the love of God that is in Christ Jesus our Lord" (Romans 8:39).