It is always so traumatic to lose a family pet, and it's even harder when someone in the group is being less than supportive. I'm not a psychologist so I can't make any real guesses about your father - but it seems from the things you're saying that he likes attention. He seeks attention and he then gets it. Maybe he thinks this is the only way he gets attention, and he gets rewarded by attention when he does it, so he keeps doing it. Sort of like a 2 year old. He does what works. He gets annoyed when something else (like the cat) is getting his attention so he intrudes on it.
People do things that bring them rewards. They don't do things that are useless. So he must be getting some reward out of this.
So if it was me temporarily "stuck" with him, here's what I would try to do.
I would try to find a way each day to give him positive attention. I don't know him to guess at how this could be done, but with my own father I could play a game with him, or sit down to talk with him, or ask him a question in an area he likes to talk about. I could brainstorm ideas with you if you wanted. So that way he IS getting some attention.
Then, when he acted out, I would give him NO attention. Not negative attention, because that is still attention. So no frowning or sighing or eye rolling. I would simply pretend he didn't exist. That is one of the most annoying things possible for most humans. That TED talk I just posted in the stress relief area talks about that. So simply act as if he has turned transparent. Be happy in your own little world.
If you suck all energy out of his bad behaviors - and at the same time provide tangible rewards for good behavior - it might start to make a tiny difference.
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