You have to make an application to muncipal corporation for correction in date of birth 

2) enclose an affidavit as to correct date of birth 

3) enclose documentary evidence like hospital records as to correct date of birth 

4) if authorities refuses you would need court orders to rectify the mistake in date of birth 

Since it is a very old case you cannot be able to get the birth certificate from the authorities concerned especially if her birth was not registered with them.

Her school leaving certificate itself would be sufficient to prove her date of birth and the passport can be made by that date itself.

You may ignore the gram panchayat issued certificate.

It is not a case of correction of birth certificate , you have to obtain birth certificate  of municipal authority Bhor as her birth is not registered yet.  May be 70 yrs back, there is no Bhor municipal authority. But as and it was formed, the  municipal authority notifies that all birth registered in panchayat should to re-registered with municipal authority.  Claim that you did not get the  re-registered with municipal done. Following is the procedure under Births and Death Registration Act for obtaining birth certificate …

1. Apply to municipal authority as per the date of your actual birth. Municipal authority will give a certificate that no such birth is registered on that date.
2. Submit an application to the Executive Magistrate/Tahsildar/MRO for direction to municipal authority for birth certificate  on the said date with following  .
3. A notarized affidavit stating that you birth took place at home on the said date and the same is not registered.
4. No birth registered certificate issued by municipal 
5. Proof of date of birth from Aadhar and other document.
6. Executive Magistrate/Tahsildar will give direction to municipal authority for issuing birth certificate.
7. Take that direction to municipal authority and apply for birth certificate  on said date.
8. You will get required birth certificate on payment of Rs. 50/- fee to municipal 
9. Explain this procedure to local Advocate.

You can only rectify the same if it's a clerical error in subsequent records after correct birth date

-  In urban areas, the authority to issue birth certificates lies with Municipal Corporations or Councils, and the Gram Panchayats is not a competent authority to issue the same. 

- Since, her date of birth is correct and common in SLC , Adhar and PAN card, then she can apply for getting the birth certificate from the office of the Municipal Corporation /Registrar. 

Under The Registration of Births and Deaths Act, there are provisions for correcting errors in the birth register and correspondingly in the birth certificate. You need to prove to the authorities that there exists an error.

to issue a birth certificate you can go to a nearby municipal corporation or to an SDM office.