Database model: doubly linked list
I'm not sure I understand your question right, but:

If I understand right, this is a tree that has children ordered. Also the creation of children is monotone, that is no children are deleted.
In these cases, in relational databases I used to have:


Id
parent's Id
child order (first child is 1, second 2, etc.)
child count (count of my children, only needed if you want "last child")
acceptor, ...


Key's are ( Id ) &amp; ( parent's ID ; child order ).

In this case:


Previous sibling is ( parent's Id ; child order-1 )
Next sibling is ( parent's Id ; child order+1 )
First child is ( Id ; 1 )
Last child is ( Id ; child count )
Parent id ( parent's Id )


I hope I helped.