TYPO3 Core

AFAICS copying children together with the page record currently is not possible, since the whole translation process is not based on a copy action but on a simple call to process_datamap:

        if ($Ttable === $table) {
            // Get the uid of record after which this localized record should be inserted
            $previousUid = $this->getPreviousLocalizedRecordUid($table, $uid, $row['pid'], $language);
            // Execute the copy:
            $newId = $this->copyRecord($table, $uid, -$previousUid, true, $overrideValues, implode(',', $excludeFields), $language);
            $autoVersionNewId = $this->getAutoVersionId($table, $newId);
            if (is_null($autoVersionNewId) === false) {
                $this->triggerRemapAction($table, $newId, [$this, 'placeholderShadowing'], [$table, $autoVersionNewId], true);
            }
        } else {
            // Create new record:
            $temporaryId = StringUtility::getUniqueId('NEW');
            $copyTCE = $this->getLocalTCE();
            $copyTCE->start([$Ttable => [$temporaryId => $overrideValues]], [], $this->BE_USER);
            $copyTCE->process_datamap();
            // Getting the new UID as if it had been copied:
            $theNewSQLID = $copyTCE->substNEWwithIDs[$temporaryId];
            if ($theNewSQLID) {
                // If is by design that $Ttable is used and not $table! See "l10nmgr" extension. Could be debated, but this is what I chose for this "pseudo case" 
                $this->copyMappingArray[$Ttable][$uid] = $theNewSQLID;
                $newId = $theNewSQLID;
            }
        }

Since $Ttable (pages_language_overlay) differs from $table (pages) the condition is false, thus just creating a new record without taking care of any special localization configurations.