I would suggest taking the Lynx City Bus #50.
For a grand total of $40 (or less, not sure about childrens' fares) you can get there and back.
Go to
www.golynx.com and look up the schedule for #50.
It departs the TTC about every half hour starting pretty early in the morning. Each person will pay $2.00 each way (correct change). (Children may be less).
So on the day you wish to leave, take a bus from your resort to Magic Kingdom, then take the monorail over to the TTC. From there ask the first CM you see how to get to the Lynx Bus Stop.
Wait there. When bus #50 to Downtown Orlando arrives, get on and pay your fare. Tell the driver you want to get off at Sea World.
The bus will proceed through many stops, one of them being DTD West Side. (If you happen to be staying at SSR, you can walk to the DTD stop instead of going to TTC. Any other resort will not have transportation to DTD before 9:30am.). After it leaves Disney Property, it will make a couple more stops, then it will get on I-4. After you leave I-4, you will get off at the 3rd stop. This is right in front of the Renaissance. You then get off the bus, walk across the SeaWorld parking lot.
When leaving SeaWorld, the return bus stop will be across the street from the stop you got off at. Wait on the #50 bus marked TTC. You then ride the bus till you get back on Disney property. You can choose to get off at DTD West Side and take a Disney bus to your resort, or you can go all the way to the TTC, then take the monorail to Magic Kingdom to get a bus back to your resort. Just decide which is easiest for you.
