That is a tough one. I notice one of my dogs picks up on all our family emotional pain. But she just gets sad or nervous (no worse than that). Just a guess here but maybe try a grounding meditation in the morning and then again at night? Maybe that will lower the negative out of your home so that it doesn't leak out to animals?
I've had the same problem with my pets suffering because of my own illness. It made me feel awful.
Have you tried putting a permanent shield around each of your pets with the stated intention of allowing the light through, but keeping out all negativity including physical illness? I guess you'd need to include relatives and maybe friends pets also, after what happened with your grandma's bird.