Now, you're cookin'!

This may be an ideal situation to get things into the right hands before people have to decide much later, if you know what I mean...
One of the things that you could do would be to speak with all about having your mom's things and needing to do something with them. You could ask them what would be a fair way of distributing them if some or all of them have an interest. You could make a list of the items, maybe even with pictures, and distribute it to the children.
I know that when one of my dad's brother's died, my dad and his other remaining brother just flipped coins to decide on who got what. I am sure that there are other, creative ways to make sure that the person who really needed or wanted something could have opportunity to obtain it.
I don't really know the ideal way to deal with this. But, I do know that if it is something that is from a part of the family history, then it would help to have a good way of making sure that things are passed down to those who really want them.
Maybe someone else will come along who has some ideas also!