Upvote:3
Yes, the two weeks in Cayman uses up some of your 90 day time. The 90 day clock starts from the day you enter the US, and continues counting even during time you spend in the Caribbean islands.
Upvote:6
Your proposed itinerary is not legally permitted under the Visa Waiver Program.
When you first enter the US, you will be stamped in WT status for 90 days from the date of entry. This represents the so-called "90 day clock" that begins counting. If you travel to Canada, Mexico or the Caribbean during this time, and return to the US, you can only be readmitted for whatever time remains of the 90 days, which continued counting down while you were in the Cayman Islands.
Unfortunately, your itinerary would have you remain in the US until day 98 past your arrival, eight days longer than would be permitted.
You have a few options at this point:
You can rearrange your itinerary so that your visit to Cayman Islands is either at the beginning or at the end of your trip, so that your time in the US is continuous.
At the beginning is fine, because the 90 day clock does not start until you enter the US (provided, of course, that you do not transit the US to reach Cayman). At the end is also fine, because you are considered to have departed the US when you leave the US for the Cayman Islands and then go directly home. (And even if you have to transit the US to return home, the 90 days will have expired, so you should have no problem there. Remember that the purpose of the 90 day rule is to prevent visa runs, not to prevent people from going home.)
You can cut your trip short.
You can obtain a US visa. With a visa, you can stay in the US for up to 6 months on each visit, and the 90-day clock does not apply. Note that you will need two entries, but most countries' nationals get multiple entry visas anyway.