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Your long term vacation lease agreement is going to be governed by the same landlord/tenant statute that applies to residential leases, however, the specifics of the lease contract are going to likely be different from what you would normally expect to find in a residential lease agreement.
(The terms matter, and the specific clauses and language in the lease is going to be enforceable).
Regarding the specific issues that you identified here, the tenant appears to be threatening a breach of lease claim.
However, all of their claims (real or imagined) are being addressed by moving them to a similar unit.
If the tenant really wants to push this matter to a conclusion, they could force it to court, where a judge would require them to show that the second unit was somehow not comparable to what they bargained for. (Which is a difficult standard if you are talking about simply moving them from one unit in the same complex to another - I assume with the same area).
If they decide to breach the lease and leave early anyway, they are responsible for rent just like under a residential lease:
Until: (1) the end of the lease term; or (2) a new tenant takes possession of the rental unit. The landlord must make reasonable efforts to find a new tenant, but the tenant is responsible for the costs of finding the new tenant (advertising, turning over the unit, etc.).
Short of having this issue end in a lawsuit, you can try to mediate the dispute with them - contact your local bar association and request referrals to mediators, a third party neutral can often help you reach a mutually agreeable resolution. Use the bar association's referrals to contact a mediator or two, the mediator will then contact the other party to set up a mediation session, and you can go from there - hopefully resulting in a formal or written settlement agreement, and save yourself the time and expense of litigation.