Inheritance law in india wrt self-earned and ancestral property

X bought agri land. He died intestate. His 6 sons divided (partitioned) the property. Son A got a share (property F). Son A had also acquired (self-earned) property (property G) in his life time. Son A died intestate and has 1 son (married, has a son), 1 daughter (married, has 1 daughter) and 1 more daughter (unmarried) and a wife (widow). At this juncture, what are the rights of son A's window (wife) with respect to properties F and property G, if the heirs of son A are willing to partition property F and register property G in 4 names. X and A were Hindus (Lingayat). I do not know if this suffices to invoke the HUF law related to Inheritance. I do not know if the Mitakshari is applicable here. Or something else. Please clarify as to the rights of the Widow. After the division, can she sell her share without the consent of her 3 children, both her partitioned part of property G and her undivided share of property G?