Partition deed is not required
You can make a family arrangement deed where both you and your sister will agree about the distribution of your father's estate between you two
The family arrangement deed can be made on a stamp paper of Rs 500 only and is required to be signed before a notary
The notary can be called at home to do the notorial act since your sister cannot travel. Ofcourse he will charge his fees for that
Once the family arrangement deed is executed the parties can then register release or relinquishment deed in favour of each other such that they become exclusive owners of their respective properties agreed under the family arrangement deed
The release deed attracts only Rs 200 in Maharashtra
For other states you will have to inquire with local lawyer
The release deed has to be registered which too can be done using the POA of your sister
The POA can be signed before the sub registrar. Under the registration act the sub registrar can come to your house if the executant is not able to appear personally before him due to a bodily ailment
The release deed has to be registered before the jurisdictional sub registrar. For eg for the Mumbai property the release deed has to be registered before the Mumbai sub registrar of assurances
A formal legal heirship certificate will be needed in order to complete the flow of title so that you or your sister dont face any problem in future at the time of sale of your respective properties