Hmm .. combining a temporary TABLE with REPLACE seems to do the trick.

DROP TABLE IF EXISTS t_tree_insert, _t;

CREATE TABLE `t_tree_insert` (
    `f_node_id` INT(10) UNSIGNED NOT NULL AUTO_INCREMENT,
    `f_parent_id` INT(10) UNSIGNED NULL DEFAULT '0',
    `f_name` VARCHAR(200) NOT NULL,
    `f_sort` FLOAT NULL DEFAULT NULL,
    PRIMARY KEY (`f_node_id`),
    UNIQUE INDEX `sort` (`f_parent_id`, `f_sort`),
    INDEX `f_parent_id` (`f_parent_id`),
    FULLTEXT INDEX `f_name` (`f_name`)
)
COMMENT='test tree move operations'
COLLATE='utf8_general_ci'
ENGINE=InnoDB
AUTO_INCREMENT=0
;


insert into t_tree_insert values
    (130, 1, 'other array', 1)
  , (142, 2, 'B06', 1)
  , (143, 2, 'B2L', 2)
  , (144, 2, 'B2M', 3)
  , (200, 2, 'INSERT', 3.5)
  , (145, 2, 'B2N', 4)
  , (146, 2, 'B2O', 5)
  , (150, 3, 'other array', 1)

;

select * from t_tree_insert order by f_parent_id, f_sort;

set @sort=0;

create temporary table _t as 
   select f_node_id, f_parent_id, f_name, (@sort:=@sort+1) as f_sort
   from  t_tree_insert as T
   where f_parent_id = 2
   order by T.f_sort
   ;

select * from _t;


replace 
   into t_tree_insert 
   (f_node_id, f_parent_id, f_name, f_sort)
   select * from _t
;
     
DROP TABLE _t;


select * from t_tree_insert order by f_parent_id, f_sort;
[download]

t_tree_insert

130	1	other array	1
142	2	B06	1
143	2	B2L	2
144	2	B2M	3
200	2	INSERT	3,5
145	2	B2N	4
146	2	B2O	5
150	3	other array	1

_t

142	2	B06	1
143	2	B2L	2
144	2	B2M	3
200	2	INSERT	4
145	2	B2N	5
146	2	B2O	6

t_tree_insert

130	1	other array	1
142	2	B06	1
143	2	B2L	2
144	2	B2M	3
200	2	INSERT	4
145	2	B2N	5
146	2	B2O	6
150	3	other array	1

probably I can even do it without a temp table...