Dealing with ordered hierarchies

I have read many articles about dealing with hierarchies in postgres
including nested sets, ltree, materialized paths, using arrays as
parentage, CTEs etc but nobody talks about the following scenario.

Say I have a hierarchy like this

1
1.1
1.1.1
1.1.2
1.2
1.3
2
2.1

In this hierarchy the order is very important and I want to run
frequent(ish) re-ordering of both subsets and entire trees and even more
frequent inserts.

Scenario 1: I want to insert a child into the 1.1 subtree. The next item
should be 1.1.3 and I can't figure out any other way to do this other than
to subquery the children and to figure out the max child ID, add one to it
which is a race condition waiting to happen.

Scenario 2: I now decide the recently inserted item is the second most
important so I reset the ID to 1.1.2 and then increment 1.1.2 (and possibly
everything below). Again this is both prone to race conditions and
involves a heavy update.

Is there a better way to deal with this or is the complexity unavoidable?

I should state that like most database reads will be much more frequent
than writes and inserts will be more frequent than updates (re-ordering)