Interesting combination of locales you'll be visiting ... as far as bathrooms go - I don't know what they are called down under, but most of the sites you'd visit have portable bathrooms (the little white plastic boxes) available - bring your own supplies and don't sit is the best advice I could offer there. On this note, I will also give you a bit of advice (dc locals - correct me if I'm wrong on this because it's been a big deal) -- if you ask in a metro station, they will open the door for you, you won't get entry without the request.

Also - once you are firm on your plans as far as date & time when you'll be arriving in DC and its closer to that date (along with info on your party size), post the information either in this thread or a new one ... it could be that there is a local or visitor that might be available to meet up to say hello and do that driving for you around the monuments.

I totally understand the reluctance to too deep into the city. I made a "keep left" sign for my rental in NZ, with some reminders about the right turn being the long turn since I wasn't accustomed to driving on 'that' side of the road. I still made one big "oops", quickly corrected with thankfully no cars in my way, right after I took this last rental car out.

Enjoy your trip.