The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

ALTER TABLE `child1` ADD INDEX `child1_idx_parentid` (`parentID`);
ALTER TABLE `child2` ADD INDEX `child2_idx_parentid` (`parentID`);
ALTER TABLE `child3` ADD INDEX `child3_idx_parentid` (`parentID`);
ALTER TABLE `parent` ADD INDEX `parent_idx_parentid` (`parentID`);

The optimized query:

SELECT
        child1.child1ID,
        child2.child2ID,
        child3.child3ID 
    FROM
        parent 
    LEFT JOIN
        child1 
            ON child1.parentID = parent.parentID,
        
    LEFT JOIN
        child2 
            ON child2.parentID = parent.parentID,
        
    LEFT JOIN
        child3 
            ON child3.parentID = parent.parentID 
    WHERE
        parent.parentID = 1