I know that I should be ignoring W's texts, but I really really like getting them.
It is not about ignoring the text. It is about how you respond. Steve's advise above is dead on. Read it again.
You are not busy enough. Focus on doing things that you enjoy. Things that you want to do. Things that you need to do. Get out of your head. Be in the moment.
Next time W text about the dog: H:"W, thanks for sharing. I plan on taking him to the park when I get back."
Take the dog to the park. (Multiple times a day). Do not invite W. If she asks to go, say yes.
"What is best for my kids is best for me" Amor Fati Link to quotes: https://www.divorcebusting.com/forums/ubbthreads.php?ubb=showflat&Number=2879712