i am currently pre-law in college and we went over this type of law last year... so here it goes....

as long as the computer belong's to your family then it is legal, it is similar to hiring a private eye to spy on your wife.

however, it is more difficult to use the information gained in court because unless you could prove that you did not fabricate the evidence (which with computers is very easy) you would not be able to use it. the best way to do this would be to have the keylogger write to a usb key and turn the keylogger off after the conversation and don't touch the file, then bring in an expert in computer forensics who has looked at the file -- this way you have an expert witness in court. also, you may need a security camera with a time/date stamp so that you can prove that the file time/date creation time matches up with when your wife was on the computer.

i do have to agree with a previously statement though -- talk to your wife, confront her with his "evidence" and see what happens -- if she is, and you are cool with that, now you know the truth, otherwise, the rest is up to you --

good luck