OK, taking the "ask here before doing anything" advice to heart:

The W has one of our two dogs today, and said she took her for a long run. I asked when she wanted to drop her off with me.

I came home, and found that she already had left the dog at my house, without coordinating. (she still has a key)

While I had indicated that her dropping the dogs was fine (with coordination) she didn't wait for an OK from me or anything.
I feel like it's reasonable to send her a message saying

"Please coordinate with me before dropping off dogs, don't just leave them here without telling me"

Me, H-39, W-33
T11, M3
No children
Bomb 10/17 - "Not sure what she wants"
Bomb 2 12/17 - forced convo it did not go well.
W moved out 3/18
OM Confirmed 4/1
D Final 9/27/18