She's cleaning the house. It's your job to do the "man thing" and mow the lawn. If you don't want to mow the lawn, it's your job to pay someone to do it. Her comparison to "would you pay for half of a cleaning service?" is right on.

How can you expect her to pay for half of the lawn service (just because you don't feel like doing it yourself) while she's doing all of the cleaning of the house?
Take a step back and realize that she's working with you and not being unreasonable (in this case...at least).
Trevor wrote:If she is granted exclusive use of the house, then she is 100% responsible for its maintenance. If a tree falls and crushes the roof, that's another story. But yard work is no different than washing the dishes and cleaning the windows. She fails to understand the simple concept that along with rights come responsibilities.
If he didn't agree to do the lawn and set that precedent, I would agree with you.