Can your dad fax you the contract?
This is starting to become a recurring theme. I can't recall if the other situations I've read about have been through this agent or others, but I know I have read about this same thing happening with other STJ villa travelers - recently. I'll try to research the other posts and see if there's a common theme here in terms of the agency.
I guess you have to take the agency's word that it was the owner....but I suspect this happens more because so many agencies list the same villa, don't have a central booking tool (or don't check it/update it) and the villa gets double booked across two different agents - and someone has to be cancelled

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I can see it happening easily - but the agency should be judged on how they handle it. If the agency doesn't feel really horribly and doesn't take care of you as though they feel horribly, then maybe it happens too much with them and they should not be considered for future bookings. Sounds like this one remains to be seen.
Also, the "whoops, we quoted you the wrong rate" has also popped up recently on another post. I don't think it was this agency. Eventually, after a little pushing back, that poster received an email that the agent would honor the misquote - very good business.
In the case of the owners wanting the villa for themselves, that's nice - but you have a contract and you've already spent money that you cannot recover. I think you are right to stand your ground

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The agents earn a % commission off of the rental - some as much as 40% of your rate. So, the agency may be able to afford to knock off a hefty % of the rate for another villa that may be more expensive - bringing it in line with the rate of your original villa.
I would not settle for the agency just looking for another villa at the same price as the original villa if none of them compare in amenities and location. The agency may just have to "eat" this one.
If it wasn't the agency's fault and the villa owner is at fault, that owner can work something out with the agency that keeps the agency whole.
Unless the langauge in the agreement allows the agency to do this, I would check out whether this qualifies as a material breach of the agreement, for which you can be compensated - in case it comes to that - which I'm sure it won't

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Good luck!