Your relatives claims seems rather untimely. The time to dispute ownership was before your father begin interring family members there. The argument should be that they have no documentation and are estopped all these years later from making claim. It appears there is still room for your father, so you should not have to delay the burial. Worst case, your mom when the time comes can still be buried in the same plot (vertically). You should get a notarized statement from the old country boy recognizing your dad's ownership interest.
If you'd like to discuss, please feel free to call. Jeff Gold Gold, Benes, LLP 1854 Bellmore Ave Bellmore, NY 11710 Telephone -516.512.6333 Email - Jgold@goldbenes.com
You should consult an experienced litigator who has experience working with real estate disputes, as soon as possible. As the first answer points out, there may well be a defense to this claim, but this is not a do-it-yourself area. My condolences to your family on the loss of your father as well as having to deal with this issue.
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