What/where is the DMV?? Sorry, but that translates to the Department of Motor Vehicles to me :-))

My guess would be Delaware/Maryland/Virginia. My local Ace hardware store has a bunch of local mixes (ie not Scott's or a national brand). I would look for those. Failing that, try my local grass seed company:

Lawn Seeds — Allen, Sterling & Lothrop (allensterlinglothrop.com)

Most places that sell grass seed have varieties specifically for shade.

It should be noted that most turf grasses prefer full sun. Some types are more shade tolerant than others but no lawn or turf grass will do well in much shade. And also consider that the mature trees that are providing this shade are making the area under their canopy quite dry as well, another factor for a failure for a lawn to thrive.

Is a lawn the only solution? Maybe some sort of shade and drought tolerant groundcover would be a better choice.

Photos would help, as would a clarification of your location.