MySQL:unir y contar filas de otra tabla

Hay pocas opciones posibles, una de ellas:

SELECT * ,
  (SELECT count(*)
   FROM `table_votes`
   WHERE `children`.`id` = `table_votes`.`child_id`) AS `Count`
FROM `children`
WHERE `parent_id` = 20

También puede usar su consulta, pero tendrá que agregar GROUP BY :

SELECT  
 `children`.`id`,  
 `children`.`data`,  
 `children`.`parent_id`,  
 `children`.`timestamp`,  
 COUNT(`v`.`children_id`)  
FROM `children` LEFT JOIN `table_votes` `v` ON `children`.`id` = `v`.`child_id`  
WHERE `children`.`parent_id` = 20 
GROUP BY `children`.`id`, `children`.`data`, `children`.`parent_id`, `children`.`timestamp`,
ORDER BY `timestamp` ASC