Have you considered sewing it on yourself? Sure mom can do a better job, but ask her to show you and then do it yourself! We will forgive you if it is not sewn perfectly straight.
The Wolf, Bear and Webelos books have drawings at the inside of the cover. (The 1998 books did so, but not the 1999 books). The new Bear book has it on pages 20-21. The new Webelos book has it on page 458.
The inside cover of the Boy Scout Handbook shows the location for the badges.
Guess what's on the inside cover of the leader handbook...
BSA has devoted a whole pamphlet to this purpose: "Insignia Guide".
Publication number 33064.
Ask before sewing! The clerk in the scout store usually knows.