Hello Linh,
I assume you are reading and analyzing this letter.
http://marthawashington.us/items/show/87

The video I showed in class last term was this one:
http://www.imdb.com/title/tt1203829/

View online at:
http://www.youtube.com/watch?v=Pwvvv0EcWIE

And the female professor who spoke about George’s letter is:
http://www.pacific.edu/Academics/Schools-and-Colleges/College-of-the-Pacific/Academics/Departments-and-Programs/History/Faculty/Directory/Cox.html

One of the problems with analyzing his letters is this:
Martha destroyed nearly all of GW’s letters to her shortly before her death in 1802. Three letters, however, did survive. Two are printed in The Papers of George Washington, Revolutionary War Series, vol. 1, 18 June 1775 and 23 June 1775. These letters were found by Martha Parke Custis Peter, one of Martha Washington’s granddaughters, in a drawer of a small desk that she inherited from Mrs. Washington. The 18 June 1775 letter is now held at Tudor Place, home of Martha Parke Custis Peter and her husband Thomas Peter.

This website provides a good reason why she destroyed them just before she died.
http://georgewashingtoninn.wordpress.com/2009/04/05/why-did-martha-burn-her-letters/

So, in short, the only real reason why we have this letter is that Martha failed to destroy it.  As for analyzing it, the video used OTHER information, such as George showing up to the meetings in full uniform, indicating he wanted the job.  Yet, the letter clearly states to Martha that he didn’t want it.  Because we do not have many of his other letters to Martha, we are left with speculation, but it can certainly be informed and educated.

Do these links help with your paper?