IDK if it works this way with dogs, but with cats, if one of your pets dies, you should show the body to the living relatives, let them sniff it and be aware of what's going on. They will deal with it better if they know what happened than if Other Buddy just disappeared one day and they don't know if buddy is coming back.
Animals can't express themselves vocally as we do, but I'm of the belief that they feel emotions and pain the same way we do. I mean why wouldn't they..
When my first cat died, he died at the vet hospital. We elected to get him cremated.
So my other cats didn't know what happened. And the next few weeks, our living cats would wander meowing more frequently. They sensed our own sadness, but also that something was different.
When I lost my Chihuahua, my other dog and my roommates cats definitely acted a little off and we attributed it to them grieving. We also thought it could be them responding to our emotional state but we were never certain tbh
my cat let out a loud and long meow of anger and disappointment each time i brought my dogs home at the beginning and he seemed to only tolerate their presence; he didn't seem to notice when they died. he's an asshole but i love him.