Thank you. The issue here is that as a private sale, your rights are rather limited and the legal principle of ‘buyer beware’ applies, where you are expected to satisfy yourself that you are happy with the purchase before proceeding with it. The seller will not be liable for any issues which may occur after sale as the risk passes over to you after you purchase it. You will only be able to pursue the seller if they clearly misrepresented the cat, i.e saying it was black when it was white, that it had no injuries, when it came with 3 legs, or that it was of mild character when in fact it was clearly highly charged.
The issue in your case is that a lot of it can be attributed to the stress of the move, as cats are territorial animals and get distressed when their trusted environment gets changed. No one can help that or predict how bad it would be and you cannot blame the seller for it – it is just part and parcel of buying living animals. Similarly, you cannot realistically say that she lied to you about how the cat would behave if shut out because again, we are talking about a living thing, with its own brain and capable of making its decisions in that respect so no matter what the seller said, I can never be a guarantee.
On that basis, they unlikely would owe you a refund and it is a case of taking what is on offer or selling the cat on yourself to someone else to recoup these costs.
I appreciate this may not be the answer you were hoping for but it is the legal position and I hope that it at least clarifies where you stand?