Personally, I would rather drive from Norfolk to Dulles Airport and get a good routing on a single ticket than have separate tickets, one to NYC and one from NYC to Europe. If you are on separate tickets and something goes wrong with the first flight, you may well miss the transatlantic flight, and you will be the one paying for the last-minute replacement ticket--a roundtrip ticket, because if you miss that flight to Europe, the return flight will also be canceled.
There used to be, and I assume still are, some not-grotesquely-expensive hotels out near Dulles airport that provided free parking for a decent period of time (maybe about long enough for you) if you spent one night there before your flight. I live in DC and have not ever needed to take advantage of that policy, but it sounds like it's worth checking out. I realize that you do not actually need to spend a night at Dulles, but paying for a room would probably be quite a bit cheaper than paying for parking for the number of nights you will need.
And you definitely should plan to head over to Europe at least one day ahead of time. Tours are expensive on a per-day basis. You don't want to sleep through the first 24 hours of yours, due to jetlag, etc.