The optimization process and recommendations:

1. Avoid OR Conditions By Using UNION (modified query below): In mosts cases, filtering using the OR operator cannot be applied using indexes. A more optimized alternative will be to split the query to two parts combined with a UNION clause, while each query holds one part of the original OR condition.
2. Avoid Subqueries (query line: 41): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
3. 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.
4. Replace In Subquery With Correlated Exists (modified query below): In many cases, an EXISTS subquery with a correlated condition will perform better than a non correlated IN subquery.
5. Use UNION ALL instead of UNION (query line: 34): Always use UNION ALL unless you need to eliminate duplicate records. By using UNION ALL, you'll avoid the expensive distinct operation the database applies when using a UNION clause.

Optimal indexes for this query:

ALTER TABLE `qryAccJunctionDetails` ADD INDEX `qryaccjunctiondeta_idx_childaccountid_parentaccountty` (`ChildAccountID`,`ParentAccountTypeID`);
ALTER TABLE `tblAccount` ADD INDEX `tblaccount_idx_accounttypeid` (`AccountTypeID`);

The optimized query:

SELECT
        qryaccountnamesconcat_accountid,
        qryaccountnamesconcat_accountname,
        qryaccountnamesconcat_jobtitle 
    FROM
        ((SELECT
            qryAccountNamesConcat.AccountID AS qryaccountnamesconcat_accountid,
            qryAccountNamesConcat.AccountName AS qryaccountnamesconcat_accountname,
            qryAccountNamesConcat.JobTitle AS qryaccountnamesconcat_jobtitle 
        FROM
            qryAccountNamesConcat 
        WHERE
            (
                (
                    EXISTS (
                        SELECT
                            1 
                        FROM
                            qryAccJunctionDetails 
                        WHERE
                            (
                                qryAccJunctionDetails.ParentAccountTypeID IN (
                                    1, 2
                                )
                            ) 
                            AND (
                                qryAccountNamesConcat.AccountID = qryAccJunctionDetails.ChildAccountID
                            )
                    )
                )
            )
        ) 
    UNION
    DISTINCT (SELECT
        qryAccountNamesConcat.AccountID AS qryaccountnamesconcat_accountid,
        qryAccountNamesConcat.AccountName AS qryaccountnamesconcat_accountname,
        qryAccountNamesConcat.JobTitle AS qryaccountnamesconcat_jobtitle 
    FROM
        qryAccountNamesConcat 
    WHERE
        (((qryAccountNamesConcat.AccountID) IN (SELECT
            tblAccount.AccountID 
        FROM
            tblAccount 
        WHERE
            tblAccount.AccountTypeID IN (1, 2)))))
) AS union1