Parking at the port in Baltimore is a breeze. It is located right off I-95 (I believe you take exit 56 - but I would get a triptik to verify that). Follow the signs and you will arrive at the Cruise Terminal. Parking is located adjacent to where the Grandeur will be docked. If you have a lot of luggage - you might want to swing the car around to the ship and drop off luggage and passengers and the driver can than park and walk back.
As for trying to shop, spend some quality beach time and see the ruins - I don't think you will have time. You will need to decide if seeing the ruins is a priority or beach and shopping is more important. In order to see the ruins you will need to first take a ferry to Playa del Carmen, then get transported to the ruins. It is definitely an all day excursion. There are some fantastic beaches in Cozumel. We have done extensive research on all the ports you will be visiting. You might want to check out our reviews as well as other cruisers at www.portreviews.com
. You can also go directly to the Caribbean port reviews:
Interestingly Cozumel is our featured port this week at CruiseReviews.com.
Now, as for disembarking from the ship. Those with early flights are usually the first off the ship. Those with their own travel arrangements via car are usually the last off. You will be asked to complete a form about halfway through your cruise indicating your post cruise travel plans. If you want to get off early - one way is to just list an airline and flight number that departs before noon as your plans. Another option is to keep your luggage with you (if you don't have too much and can handle taking it off the ship yourself). Don't pack it and put it outside the last night as requested. When they call the first colored tag group to depart - just walk right off the ship with them.