Dug - it is not unreasonable, but if you really think it is necessary then there is still some doubt in your mind. I think its possible that if you require one of him, he will fail it, but not because he was physically involved with her. Instead, he will likely fail it because its going to be hard for him to remember details of all they talked about, and when he's questioned he's going to get confused. Then failing the test, you are going to think he was up to more than he might have been.
I don't know if this will get deleted or not, but there is a site called Marriage Builders. They have a general questions II area in their forum where LOTS of people advocate polygraph tests. If you can find them, run your question by them over there and see what they say after hearing the whole story.
Personally I would not require it...but that is also because I have doubts as to their accuracy...just my own opinion.
