I'm not in the Bethesda area, but I can answer some of your questions.
Rate: it can vary based on how many hours per week you need, because after 40 hours, you are required to pay time and a half. Each family will probably pay $8-10 per hour to start. This is the base rate for the first 40 hours.
Hosting duties: some families rotate houses and some don't. If you decide to swap hosting duties, I suggest doing so every two weeks or every month. If you swap weekly it will be a pain (lugging diapers, high chairs, pack n play, etc) rotating daily would be an absolute nightmare!! The kids need routine.
Pros for hosting:
You don't have to do drop off.
Your child gets to sleep in his/her bed
Cons:
More wear and tear on your house, toys
Possibly higher utility bills
Misc purchases:
A double stroller
Two high chairs
Two bouncy chairs
Pack n play
It's great if the host has a room for the "guest" baby to sleep in. It doesn't have to be an actual bedroom, just a quiet, relatively dark room.
Also nice if the host family is in a walkable area, especially when the kids are infants.
Host family will need to be mindful of baby proofing.
Very handy if the host family has a dedicated room for baby toys.
In shares, sometimes the nanny is allowed to pick both of her weeks of vacation. This is because it can be difficult to coordinate with two families when trying to plan her own vacation.
Keep in mind things like pets when looking for another family and/or deciding who will host.
Let me know if you have more questions. Happy to help.