Hi Jess,
You say you want to spend the first week in Bangkok and the second week on an island.
If you do a lot of shopping in Bangkok (as you say you will) I'd suggest that you leave it at your hotel in Bangkok and come back after the island trip and pick it up. This may mean spending another night in Bangkok at the end of your trip, but probably better than carting stuff with you to the island destination.
Otherwise, I'd reverse the order and do Bangkok last.