This property basically belong to three people, out of which one person is reported to have died intestate.
In order to ascertain the inheritance of his share in the property, a legal heir ship certificate has to be obtained by giving an affidavit duly attested by Indian consulate/Official of Indian embassy of your country, after which you can apply for legal heir ship certifiate in India before the concerned revenue department based on the said affidavit and the death certificate of your father and copies of the sale deed, revenue taxes receipt and other relevant papers of the property.
After that your mother can execute a popwer of attorney deed in favor of any close relative who is a resident in India, by getting it duly attested by the Indian consulate or a local notary public, send it to the power agent by sealed cover, who will then present it before the concerened sub sregistrar and get it adjudicated.
Once the POA is adjudicated, if the buyer is ready then you along with the power agent can sell the property jointly by executing a registered sale deed in favor of the propsecive buyer .
Relinquishment deed executed by your mother at USA will not be considrered as a legally valid document and also a foreign citizen cannot execute a power of attorney deed in favor of another foreign citizen.
You and your mother both are foreign citizens.
You can consult an experienced lawyer in India where the property is situated and proceed as per further suggestions made.