Even though it's usually a zoo, I'd do metro for getting back to Alexandria after fireworks. The yellow line will probably be less crowded than blue, so sitting somewhere east of the Washington monument and walking to l'enfant or archives afterwards will probably work well if you want to avoid excessive crowds getting on a train. But, the best seats are west of the Washington monument and over to the Lincoln memorial, imo. I haven't been down for several years on the 4th, but metro at that end was always crazy. If you're ok with just hanging out for an hour or so after the fireworks then maybe doing that and using the blue line might be ok after some crowds clear out. I used to always park on the shoulder along some of the roads on the VA side of the river and walk to the Lincoln memorial, but they kept taking away more and more of that parking.
A lot of streets in DC will be blocked on the 4th making parking more difficult.
The 7 day pass might be ok. Just depends on how much you think you'll ride. But with 10 people, it's going to be expensive. There's no family pass. Each individual is supposed to have a pass. Maybe a couple of your youngest can ride free, but I'd drive downtown on days other than the 4th with that many people.
Did you check the union station parking garage? That might accommodate larger vehicles.
