You should be absolutely fine to make the connection with 3h00, and since it's on one ticket you get IRROPS protection. It may be worth calling UA to ask for mercy and a different routing, but I would not pay more than about $100 to get out of this.

Take a car from DCA; should never be more than an hour door to door, and maybe $100 on the absolute worst day (from downtown I usually paid ~$60 and $100 was the worst; similarly about 0h40 most days, never more than an hour). Do NOT bother with Metro - it's a mess, doesn't go to IAD anyway, and will be much slower than driving.