Yes, sadbuthopeful,
I was wondering the same as coffeedrinker.
If you trust this woman because you have had contact with her, it would look like you don't trust her now. Well, that is how I would take it, if you were to ask me to sign something.
I do understand your concerns though, if the friend's wife knows of the problem and agrees to make sure the kids are safe, well, that could be a good thing.
I would thank her profusely for making this easier on you and your mind.
My experience with my ex, I could not let the kids spend the night with him unless I knew the girlfriend. We spoke, she cares for the children and has one of her own. So, one night when there was a problem, she called me immediately and I went to pick them up.
I am still grateful to her for being honest with me, and calling me that night.
Beth