2

If you split your query into four parts using UNION ALL, then the order is at your leisure:

    SELECT 1 AS Idx, ICAO_Ident AS ID, Location_Identifier AS LocID, Official_Facility_Name AS Name, Landing_Facility_Type AS AptType, Associated_State_Post_Office_Code AS State, Associated_City_Name AS City FROM APT WHERE `Location_Identifier` LIKE '%$fix%' 
UNION ALL
    SELECT 2 AS Idx, ICAO_Ident AS ID, Location_Identifier AS LocID, Official_Facility_Name AS Name, Landing_Facility_Type AS AptType, Associated_State_Post_Office_Code AS State, Associated_City_Name AS City FROM APT WHERE `ICAO_Ident` LIKE '%$fix%'
ORDER BY Idx, ICAO_Ident
1

It depends on what you have. In some cases, redirecting to a different page after the form post can prevent the issue, because they would be refreshing the page to which they were redirected.

But if you go back with the browser, then that can be circumvented as well. In that case, storing a session token can help. After you post, store a token. If you refresh and the token is set, do nothing. When you access a certain page, you can clear the token if you want.

Posting through AJAX might be an option too, because refreshing the page wouldn't trigger the event, only clicking a button would.