UPDATE: I added an CONSTRAINT DEFERRABLE to the create table, which renders LanX comment obsolete. Sorry about that./UPDATE

This is not for Oracle MySQL, I think (I didn't find the necessary functionality). This is just for fun, therefore Postgres :P

This won't work for you but you expressed some interest (or what I took to be interest) in the CB so here goes:

Below is the (p)sql-inside-bash that I cobbled together; I inserted the database-output in the script ( /* commented out */ ) for better reading.

#!/bin/sh

t=ctetree

echo "

\set insert_location 2.5

begin transaction;

drop table if exists $t ;
create table         $t (
   f_node_id   int primary key
 , f_parent_id int
 , f_name      text
 , f_sort      float
 , constraint tree_parent_sort_uniq_idx unique (f_parent_id, f_sort) d
+eferrable
);
insert into $t values
    (142, 2, 'B06', 1)
  , (143, 2, 'B2L', 2)
  , (144, 2, 'B2M', 3)
  , (145, 2, 'B2N', 4)
  , (146, 2, 'B2O', 5)
;

\echo -- base data:
table $t;

/* -- base data:
   f_node_id | f_parent_id | f_name | f_sort
  -----------+-------------+--------+--------
         142 |           2 | B06    |      1
         143 |           2 | B2L    |      2
         144 |           2 | B2M    |      3
         145 |           2 | B2N    |      4
         146 |           2 | B2O    |      5
  (5 rows)
*/

insert into $t values (394, 2, '*Inserted 1st*', :insert_location);

update $t set f_sort = floor(f_sort)+1 where f_sort >= :insert_locatio
+n; 
/* THIS BETTER REPLACED BY... see my later posts downstream */


\echo -- new begin state, after 1st insert and renumbered:
table $t order by f_sort;

/* -- new begin state, after 1st insert and renumbered:
   f_node_id | f_parent_id |     f_name     | f_sort
  -----------+-------------+----------------+--------
         142 |           2 | B06            |      1
         143 |           2 | B2L            |      2
         394 |           2 | *Inserted 1st* |      3
         144 |           2 | B2M            |      4
         145 |           2 | B2N            |      5
         146 |           2 | B2O            |      6
  (6 rows)
*/

with inserted as (
   insert into $t values (395, 2, '*Inserted 2nd*', :insert_location)
   returning f_sort
)
 update $t set f_sort = floor(f_sort)+1 where f_sort > (select f_sort 
+from inserted);

\echo -- after 2nd insert
table $t order by f_sort;

/*  -- after 2nd insert
    f_node_id | f_parent_id |     f_name     | f_sort
   -----------+-------------+----------------+--------
          142 |           2 | B06            |      1
          143 |           2 | B2L            |      2
          395 |           2 | *Inserted 2nd* |    2.5
          394 |           2 | *Inserted 1st* |      4
          144 |           2 | B2M            |      5
          145 |           2 | B2N            |      6
          146 |           2 | B2O            |      7
   (7 rows)
*/

update $t set f_sort = floor(f_sort)+1 where f_sort <> floor(f_sort);

\echo -- after 2nd insert - renumbered
table $t order by f_sort;

/*  -- after 2nd insert - renumbered
    f_node_id | f_parent_id |     f_name     | f_sort
   -----------+-------------+----------------+--------
          142 |           2 | B06            |      1
          143 |           2 | B2L            |      2
          395 |           2 | *Inserted 2nd* |      3
          394 |           2 | *Inserted 1st* |      4
          144 |           2 | B2M            |      5
          145 |           2 | B2N            |      6
          146 |           2 | B2O            |      7
   (7 rows)
*/

--
 --  remove rows 2 and 3,  and insert them after the row where f_sort 
+is 5.
--

\set location_to_insert 5

\echo -- initial:
table $t order by f_sort;

/*  -- initial:
    f_node_id | f_parent_id |     f_name     | f_sort
   -----------+-------------+----------------+--------
          142 |           2 | B06            |      1
          143 |           2 | B2L            |      2
          395 |           2 | *Inserted 2nd* |      3
          394 |           2 | *Inserted 1st* |      4
          144 |           2 | B2M            |      5
          145 |           2 | B2N            |      6
          146 |           2 | B2O            |      7
   (7 rows)
*/

create temp table _t_$t ( like $t including all );

\echo -- intermediary 1, empty temp table (to receive deleted rows):
table _t_$t order by f_sort;

/* -- intermediary 1, empty temp table (to receive deleted rows):
   f_node_id | f_parent_id | f_name | f_sort
   -----------+-------------+--------+--------
   (0 rows)
*/

\echo -- with deleted -> d. rows inserted into tmp table

with deleted as (
  delete from $t where f_sort in (2,3)
  returning *
)
insert into _t_$t select * from deleted;

\echo -- intermediary 2 (filled with the deleted rows):
table _t_$t order by f_sort;

/* -- intermediary 2 (filled with the deleted rows):
    f_node_id | f_parent_id |     f_name     | f_sort
   -----------+-------------+----------------+--------
          143 |           2 | B2L            |      2
          395 |           2 | *Inserted 2nd* |      3
   (2 rows)
*/

\echo -- with updated -> rows inserted in main table
with updated as (
  update _t_$t set f_sort = :location_to_insert + f_sort / 1000
  returning *
)
insert into $t table updated;

create temp table _t as
   select *, row_number() over () as new_number
   from (select * from $t order by f_sort) f 
   order by new_number
;

\echo -- semi-ready:
table _t order by f_sort;

/* -- semi-ready:
    f_node_id | f_parent_id |     f_name     | f_sort | new_number
   -----------+-------------+----------------+--------+------------
          142 |           2 | B06            |      1 |          1
          394 |           2 | *Inserted 1st* |      4 |          2
          144 |           2 | B2M            |      5 |          3
          143 |           2 | B2L            |  5.002 |          4
          395 |           2 | *Inserted 2nd* |  5.003 |          5
          145 |           2 | B2N            |      6 |          6
          146 |           2 | B2O            |      7 |          7
   (7 rows)
*/

update $t t set f_sort = _t.new_number
from _t
where _t.f_node_id = t.f_node_id --> join
  and _t.new_number <> t.f_sort  --> avoid writes
;




\echo -- ready:
table $t order by f_sort;

/*  -- ready:
    f_node_id | f_parent_id |     f_name     | f_sort
   -----------+-------------+----------------+--------
          142 |           2 | B06            |      1
          394 |           2 | *Inserted 1st* |      2
          144 |           2 | B2M            |      3
          143 |           2 | B2L            |      4
          395 |           2 | *Inserted 2nd* |      5
          145 |           2 | B2N            |      6
          146 |           2 | B2O            |      7
   (7 rows)
*/

rollback; -- clean up

" | psql -Xqa | less -iSR
[download]

UPDATE: slightly tweaked UPDATEs