This is going to sound weird, but, meh, whatever.
I rescued my chocolate lab just a couple of days before I started to date my EXH. Then, we got a second dog together, so he is their "fur-daddy." We kind of have a shared custody of the dogs... He takes them for a week out of the month or whenever I need him to. (Like if I'm going out of town)
However, it's often hard to get a hold of my EXH or even rely on him for anything in advance, so I will be giving a spare key to the house to my dad, who will come over and feed, water and walk the dogs if I can't get in touch with my EXH, or he can't take them. I know that he's moving at the end of the month, so I'm not sure how his schedule is going to work.
Worst comes to worst, FI can always go home and tend to the dogs. We only live about 15 minutes from the hospital.