In the beginning, every concession or agreeing to do something looks like you're being a doormat. You want to stand up for everything and that there is no dent in your self-respect armor. So, you go from one extreme to the other. I am not saying you're doing it, but that the thinking process moves from one end of the spectrum to the other and is unable to parse through the gray in between.
In the case of your dogs, instead of thinking about what W needs to do, what are your values? Are you going to let the dogs starve? Are you going to let them stay sick? Make a decision from those values.
Also, can your W truly financially contribute to this right now? If no, I wouldn't push this issue. On the other side, can you financially take on this cost fully? If not, then the option would be to give up the dogs to new homes. So, think about all of that.
Always always start thinking about your potential actions from what your values are. Don't try to stick to W. Be firm, assertive, pleasant, and handle your business.
Give your W all the space that she wants, and not control her through finances or other measures. I am not saying give her a free pass, but define your actions with confidence.
yes, she has little regard for anyone else but her right now. let her take the ticket to the moon and see how things really are. She'll find those craters as soon as she gets up close.