Does it matter if she is or is not cheating? I mean, you're sleeping in separate rooms, no love life and the problem you want help with involves her purchase of new underwear?
You don't indicate if the two of you are wanting to keep your marriage intact. If you are simply staying together for the kids you are doing them a disservice. Trust me, if they are teenagers they know all is not well between mom and dad. You and your wife need to sit down and talk. Either end this charade of a marriage or get some help in resolving the issues that have you sleeping in different rooms. As long as things continue as they are, it really does not matter if she is cheating on you or not. (Not sure if it is really cheating if both parties have checked out of the relationship as you seem to indicate.)