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What is your question please?
We will be going on such a trip in April on the Solstice, it is not uncomnon we don't like to go all that way for a 1 week cruise. If done properly you keep your cabin for the 2nd leg of your cruise a popular one used to be east and west Caribbean.
The ships crew do not like passengers on the ship for the period after dissembarking, they like a clear ship for cleaning. In the States they also insist you leave the ship and go through immigration again, ie. finger prints etc. this took my wife and I nearly 2 hours on a recent back to back from Miami.
The last answer does not apply in Europe thankfully, whereby you treat your changeover day as you would in any other port of call & come & go as you please with no requirements for all the customs & immigration nonsense. Just your cruise card through the 'ding machine' at the gangway. If what Lewis is saying relates to the US as a whole, & it probably does, I for one would be reluctant to book a B2B stateside.