How do you divide up belongings that will be inherited amonst the children?

There’s a house, and then the furniture inside it, and some art work which is valuable mostly for sentimental reasons. The parent is in a nursing home, and won’t be coming back. The children need to preserve assets to pay for her care, but they also want to maximize their inheritance (none of them say this, but given the tenor of discussions, this seems to be a concern).

They want to sell the house to generate cash. To sell the house, they have to split up the belongings. Some of the furniture is extremely valuable. Some is junk. Some of the art work is much better than the rest of the work. Each child has some of the art work displayed in their homes already, but one has a lot more of the good ones. The children are spread out geographically. The parent wanted the children to bring all the art work to one place and then divide it up. Those who live far away (including the child with the most desirable art works) say this is unfeasible.

How do you divide it up? Do you hold a draft? Do you assess everything and try to give everyone equal financial value? Do you sell it all?

And just as important, how do you do this while keeping good relations amongst the siblings? Oh, and the sibling with the most good works of art has spent much more time caring for the parent than the others.