Sibling issue...

If your sibling doesn't like dogs, or anyway doesn't know this particular dog well enough to be attached to him, he may be making the poor old dog the focus of all his discontents and frustrations. *Especially* if your father lavishes all of his affection and appreciation on the dog.

(And who wouldn't. I've just lost my dog. I am empathising in spades with your father's bond with yours).

I don't know what to suggest. Have you asked directly whether animal care is a problem for your brother? That might be the place to start.

Can I ask why you moved out after so long and stopped caregiving? Was your sibling totally on board with taking over the caregiving or not so much? Do you do more than call to say hello? Sounds like this sibling is burned out and needs some respite from caregiving. I’m also concerned for the welfare of your dog. Dogs are a responsibility as well and having to care for one in addition to a disabled person is just putting more on the caregiver. Perhaps take your dog home and just bring him for visits.

Ask your sibling what you can do to help out. Come over for an hour or two a few times a week? Come over occasionally and make a meal, help clean, spend the night? Come over and do a few loads of laundry, vacuum, wash a few dishes or bring a pizza. Or maybe even arrange for a home health aide a few times a week if you aren’t able to do what I’ve suggested. I agree with your husband. Try being proactive instead of reactive.