(((HUGS))) Paul. I have lost my mum, and my dad, husband, and brother.
For the next few days your family will have a lot of paperwork to deal with. It can be overwhelming.
At this stage, get a large ring binder and put it all in there, with what MUST be done before the funeral first, things like registering the death and dealing with the funeral director. Leave anything that can possibly wait until after the funeral.
As you say, Mum is at peace, no more suffering.