Partition Agreement

My Father died in May 2023 leaving behind my mother and 2 children - son & daughter. My mother also has self acquired properties through earnings and gifted properties. My mother has made a Gift deed to my sister in 2017 out of her self acquired property. My mother again made a gift deed for one property to my name in Nov 2023, which she had also acquired as a gift 10 years ago. After demise of my father we found he has also left all his self acquired properties and bank balance making a unregistered WILL in favour of my mother. Now my mother wants to do partition deed for all properties in her name and in my father's name to both myself and my sister. Since khata/title for properties of my father is still in my father's name, mother can't do partition deed for all the properties until we get khata in name of a living member. someone suggested a partition agreement by pooling all properties as family properties and then putting properties as each member share to ensure all parties abide by sharing agreement after which we can start process of partition deed after getting khata transferred in name of a living member. Now, should we show or include the self acquired properties of my mother which she has already gifted my sister in 2017 and to me in Nov 2023 in this partition agreement as a our share under each party? If included doesn't the gift deed made exclusively of one property to me and another property to my sister get into the pool of partition and become family properties and risk the exclusive ownership myself and my sister currently hold?