Sorry it took a while to get back to this. I am not a counsellor (perhaps DV could pipe in) but from the way you describe it, the argument was never about the dishwasher. It isn't even about your W, though she definitely had a part in the escalation. This one is about you and your own feelings of rejection.
Adam, she fired you as her H. She is bailing on your M and is openly having an affair with another man. Why, oh why would you expect her to not renege on an agreement about dishwasher parts. My guess is because she is asking people to do stuff that a H would normally do.
Now that my H has moved out, I sometimes get other people to come in and do the stuff he would have done, like painting the stairs, or doing some plumbing in the kitchen. I don't ask permission and I don't apologize. Every single time I see the flash of anger in his eyes. The accusation that I should have consulted with him first because he could have managed it, or at least got it done cheaper. Then inevitable question "How much did THAT cost?". I tell him but I do so with a tone which says, non of your business, my house, my money. He scoffs then walks away.
My H is not my H. He walked away. Therefore he does not get a say in things that a H would normally have a say in. He fired me as his W. Therefore he no longer gets to act like my H.
I am reading between the lines, but you feel that by reneging on your agreement, or by asking for another opinion, she is again, firing you as her H.
so, if your W wants to waste her time (and the time of other people) getting them to come in and look at a dishwasher, let her.
"I thought we agreed to replace it, but if you want to get some more opinions then OK. Let me know when you've decided" ... or (and I would never actually say this to him) the "whatever" approach.
Anyway, something to think about.
And you are right, the only time I throw the disrespect card is when it is about the children. When this happens comms are always business like, and always by text.
Oh and Adam. I appreciate your comments on my sitch too. It has helped a lot knowing that you, and others, are listening, I appreciate the "good jobs" as much as I appreciate the (and I've got this a few times) "you [censored] up, now get back on the horse".