I really hope your mum is okay - I know its a major shock, and especially if they were close. Ive had to see and handle quite a few bodies, due to being a policewoman, and its not nice - eventhough you may not have ever met or spoken to the person involved, you're willing them to be alive when you break into their house, if you have to. It's even harder if you have had some sort of relationship with them, even if just a professional one. I dreaded my first 'sudden death', but it gets to the point where you have to look at the process of life and death as a science, and try not to get emotionally attached - sadly its not always that easy. I dont think you ever get de-senstised to it, but I've never been in the same situation twice to be able to tell.
I find telling a relative that their loved one has died much harder than dealing with the deceased themselves, because I can't help the grieving relative in the way they want me to, but at least I can treat the deceased with the respect and dignity they deserve while they're in my 'care'. And if its in suspicious circumstances, I make sure that I do my job properly to try to ensure that they get the justice and peace in death they deserve, that they werent given in life. I really hope your Mum will be okay xx