As I understand it, twofold is the adj. form of two.(you can do that with any cardinal number except one) Your troubles will be twofold = times two. In this context, double means the same. ie your troubles will be doubled.
But double has a lot of other meanings, as an adj, a double life, or a noun like something that looks the same and can stand in for it. (a stunt twofold would be silly, of course), a verb, "double your pleasure, double your fun ... etc.
So I's say twofold, when it means twice the size or strength, can be double, but double is not as often twofold.
And in your example: a twofold problem is for me a problem that has two aspects, each of which needs to be addressed, not one that is twice the size. But double trouble is twice as big as trouble alone. I wouldn't say a double(d) problem, but rather that my problems have doubled.
Does that help? (My own confusion seems to have doubled along the way.)