Writing to the other woman is a good start, because presuming you don't want your wife engaging in criminal activities, it's going to require consent from all parties, possibly including waivers.
You'll have to look into the legalities of such an arrangement, so you'll probably want to contact a lawyer. If you don't have one in your village, that's fine, because the laws governing this are likely to be national or regional rather than municipal. It is entirely possible the lawyer will advise you and your wife not to proceed. You probably shouldn't ignore this advice.