Lots of questions, so I'll just start at the top and try to work my way down.
The only reason you'd need booster seats is if you a renting a car or riding in a car at some point and want/need to use them. Booster seats can't be used on the plane or on DME and would need to be checked luggage.
If you want to have your 14-month old in a car seat on the plane, that is OK provided that the seat is FAA approved for in-flight use. It should be marked somewhere on the seat. It's not a requirement, but many children are more comfortable if they are in their familiar seat. The car seat still can't be used on the DME buses or the WDW transport buses, as there are no seat belts to secure it. If you plan to rent a car or use a car service to get to Sea World, you will need to have a car seat.
You will need to make a reservation for DME and provide them with your flight times. If you have a reservation, you will receive your tags and an information packet several weeks in advance of your departure. Put the tags on any bags you will be checking and want DME to transport from the airport to your resort. If you need the jogging stroller in the airport, you won't be checking it and won't want to put the DME tags on it. You will need to check it at the gate in your departure city and collect it again plane side in Orlando.
As far as getting from WDW to Sea World, I think Mears offers a transport option, but I don't know any details. Otherwise, a cab or car service is an option. With six people, you'd need a van cab, or limo/van from a car service.
I'd suggest browing these threads for all kinds of good info about air travel. Also check
www.tsa.gov for information about how to make the security checks at the airport go smoothly.
Good luck! It will be great.
I'm scared to death.
