Lilac,
my words will never ease the loss of your mom but i do believe SHE would definitely press ahead in a kind of silent strength.
you will always be her daughter,the same way she remains your mother.
___
now i don't know of any way to say this beyond the fact that not everyone wants people all around them when they are dying or want to burden their family w/it.
this may have been her way and in her heart her way of keeping it simple and less distressing.
my own beloved but tough as nails grandmother even said to close the door and we knew she wanted to be alone.
she didn't even want a "wake" and that's another story.
PS my dad passed on new years day the same after a quick illness.