Your first scenario, if the family was adamant about the tests I would have called too. If the Doctor would have proceeded to yell at me, we would have had a conversation about that so he was aware that it was not OK to talk to me like that.
A lot of the unreasonable requests such as your bed scenario, a lot of times patients just want their grievances to be acknowledged. The bed being uncomfortable is probably one of the most common complaints in an ER. I am very real with my patients. I will tell them "I hear you, the beds are very uncomfortable, I remember first hand. Unfortunately the nature of the ER is we have to be prepared for anything, so we have smaller beds and they aren't very comfortable, they are made for efficiency not for comfort. Trust me, if something were to happen and you needed CPR or to be rushed to a scan or another room, these are the beds that will ensure we can treat you promptly and efficiently.It sucks I know, especially when you're stuck down here for a long time. But hopefully you can understand why. Maybe I can try and find an extra pillow to help."
When I do things like that, keep it real and keep it honest but acknowledge their grievance, I very rarely have anymore problems. I can honestly say that I have always had a good rapport with 97% of my patients and their families or been able to change things around if they had gotten ugly. And I can assure you it's not because I kiss rear ends or cater to them. I just know what it's like to be on the other side and I feel it helps me to be better nurse because of it. I think the way we handle the situations and our attitudes determine a lot of how our shift will go and the demeanor of our patients.
Not always though, sometime I just have to stand there with my WTF face and will say "Seriously???" and walk away.