speaking as a person who is ridiculously stressed about housecleaners and can't bear to have them, the LW still needs to get over themselves.

here are things the LW can do:

• get over it (possibly; it might not be that easy to get over)
• what Carolyn suggests: do the cleaning, make a deal with the wife to make it feel balanced
• make an arrangement with the wife to limit the stress, eg. "I'll be out of the house doing my own thing every time they come, and you'll guarantee that the meth and the Fabergé egg and the classified weapon plans are locked up in the safe while they're here, every time."