Succession dilema

File an application enclosing with a copy of death certificate to the sub-registrar and local municipal office. The property will be in the name of your mother. 

Does this include acquiring a succession certificate from a Court?

A joint application has to be to the court by all the three legal heirs for succession certificate and you two brothers have to declare that you want to waive your rights in favour of your mother. Then, subsequently you have to appear before court registrar and you brothers have to sign in his presence to this effect and then the letter of administration will be issued in favour of your mother.

There is no need to go the sub registrar who is part of revenue department as advised to you by some member before me . This whole matter is processed by civil court and NOT by sub registrar

as your mother is the legal heir after your father demise and your mother has to file for succession certificate if it is for immovable properties then in civil court and if any deposits if any if the value exceeds 5 lakhs then you have to file in the high court of your jurisdiction 

first you have to obtain succession certificate by filing letter of administration in civil court and with the order copy you have to submit the affidavit to transfer the property in to your mother name and the sub registrar will transfer the same in your mother name with the payment if stamp duty fees and after that you have to submit mutation application to change municipal, electricity water documents into your mother name and if your intends to transfer the property into your any one name then gift deed is the best option rather then will 

After the death of your father, you all are co-owners i.e. 1/3rd share each.  Now, you want to transfer your 2/3 rd rights in the name of your mother.   Then, please relinquish your 2/3rd share in favour of your mother by executing Relinquishment Deed and get it registered in the  office of Sub Registrar.  Ypur mother would be the owner of the property by virtue of Relinquishment Deed read with sale deed which is in favour of your father. Hence, go to the office of Sub Registrar and get the relinquishment executed and registered in favour of your mother and thereafter get the property mutated in the name of your mother on the basis of Relinquishment Deed.