She (I assume) is not going to get him to do what she wants by bringing this up over and over. He's an adult who gets to choose what he does with his time. She's an adult who gets to choose what she does with her time, which means she gets to say "I'm not helping you with the yardwork." Also she should stop making herself responsible for his mood. If she feels he's not spending enough time with her or the family, she needs to make that a separate discussion and let him decide what part of his life he will carve the additional family time from.

I have to admit I wonder how he would react if he demanded she help and she said "I will not help because I don't enjoy it, but I will pay out of my own salary for a helper for you."

And if she has no discretionary income and it's all jointly managed, she needs some discretionary income.