DC native here. I agree Greenbelt station should suit your needs. It has a enourmous open parking lot and is the most easily accessible from the Beltway. It is on the less affluent side of the Maryland suburbs. If you want a station on the more affluent side, the Grovesnor-Strathmore station in North Bethesda is also convenient to the Beltway and has a huge covered parking garage.
Greenbelt is on the green line, G-S is on the red line. Since Federal Triangle is on the blue/orange/silver lines, your family will have to change trains.
If you want a straight shot, New Carolton station on the orange line is Beltway accessible with a big garage, but more east of DC on the less affluent side. On the west, the Wiehle-Reston East station on the silver line is in affluent Reston, Virginia and has a big garage, but is not as easy to get to from the interstate.
Lots of options depending on the needs of the story.