The correct answers are We were leaving for the Bahamas the next morning, but a sudden hurricane grounded all flights, I was going to relax on the beach all week until I realized I had packed my winter coat by mistake, and The resort was to have sent a luxury shuttle for us, but it never arrived.

Past Continuous (were leaving) is excellent for past arrangements.

"Was going to" perfectly captures a past intention that was thwarted.

"Was to have sent" describes an unfulfilled expectation or formal arrangement.

Why are the others incorrect?

"Would" is not used for personal, arranged plans that got canceled; it's used for habits in the past or narrative destiny.

"Was about to" must be followed by a base verb, not an -ing gerund ("relaxing").