Divorce/WAW due to my infidelity Part 2

[crdcheck]

Thanks, guys. I'm trying to find the right balance between not bickering and being assertive. Prior to finding DR and this site I would have given in on everything as an apology for my bad behavior, hope to prove my good-ness to her. I'm not digging in just to dig in or coming up with weird hypotheticals to push her buttons but she sees any view not aligned with her own to be me refusing to compromise.

Onto the dog, she offered shared custody but that seems like a huge pain - D3 will be exchanged at school (in theory W and I won't ever see the others' place) so dog would be separate, we won't be living close to each other and the dog needs a walk during the day so multiple dog walkers. I'm definitely open to taking the dog when W goes on vacation but every other day etc. seems really time-consuming. If I were single I wouldn't have gotten a dog so I don't really want to be the full-time dog dad. I know my parents would take the dog (and treat her better than we do) so... yeah, I can see why W would not like what I'm suggesting but it also seems like this is part of divorce - we aren't on a team anymore.

I saw on another thread that someone was saying that women don't move out for space, they move out to be with someone else. Wondering if that is the deal here... I mean, it doesn't really matter but would help me to understand her rush.

Side note, while I was out with my brother looking at homes yesterday W called from some store to ask if I wanted her to pick up kitchen utensil holders. Brother said that's the nicest he's ever heard her speak to me. Weird times - she hates me, she's nice to me, she's cold to me... etc.