And if she doesn't, you:

Stop acting like her husband. She doesn't act like your wife and may never have.

Stop feeding her supply, doing her errands, doing the dishes, helping around the house, being kind to her, giving her compliments, giving her affection, saying I love you (do you? Can you love a person who doesn't give back?), etc etc.

Simply remove yourself from the position as her husband, while continuing to occupy the same house. It's your house, no need to move or do anything drastic. But let her know that from now on, you two are co-habitating, not pretending to be married any longer.

As far as the dogs, call one of her dog friends. Tell them to come take the dogs. Don't ask W or wait for her to do it, just call them and say "Come get it." End of story. No excuses or reasons or threats or else's.

Z, I'm sorry that it's come to this. I didn't realize that NPD was unfixable. That is a tragedy.

It's just as much of a tragedy to be a people pleaser married to one and continue to try and fix it.

For the sake of you and your kids, mentally remove yourself from her selfish tornado and work towards some peace of mind.

Honey

P.S. When we talk about "needs", we're talking about emotional needs, not physical ones. She can't argue that one away, Bube, now can she!