I'm another "local" although I live about 35 miles south of DC, I work in DC so I know the commute. It ain't fun that is for sure!
I agree that seeing both Mt. Vernon and DC in one day is really not recommended. You can do it if you do commando style and stick to your time schedule. However, traffic in DC can be a nightmare ESPECIALLY if a group decides to do a protest or something, then streets will be closed or at least crammed with heavy traffic.
I think DC is the only place with a 4-hour rush hour!

I wish I was kidding! Traffic will start to get bad somewhere around 3:00 PM and will just get worse (and like someone said - God-forbid there is a an accident somewhere - you'll be sitting in traffic for hours!)
If you decide to do Mt. Vernon - that can take a few hours (especially since they've opened a new museaum too). After Mt. Vernon stop in Old Town Alexandria and get a bite to eat. Lots of great places on King Street towards the water! Some of my favorites: The Wharf (great Seafood); The Fish Market (another great seafood place); Il Porto (Italian); Austin Grill (Tex-Mex); just to name a few.
Here's a website for Alexandria:
http://www.funside.com/
Here's a couple for DC:
http://www.dctours.us/;
http://www.historictours.com/washington/;
http://ahp.gatech.edu/dc_map.html
As for places to eat in DC - Old Ebbitt Grill is my favorite - I've never had a bad meal there (from beef to seafood - everything is delicious!!).
Have fun!