Restating the question:
A is the husband and B is the wife.
A has some properties which are ancestral, and which he has inherited or succeeded by proper legal documentation.
A and B are alive. What is wife's right ? Answer: Zero.
A is no more. B is alive. No children.
Answer: B becomes the successor fully.
A is no more. B and her children (X number) are alive.
Answer: There is a notional partition on the date of the death of A, who too had a share in the property alongwith the children of A. Thus there are X+1 coparceners.
A had his share, which is succeeded by B and X number of children.
So the share of B will be only 1/X=1 of 1/X+1 share of the husband. The remaining will be equally shared by X number of children.
For clarity sake, it is assumed that A and B had 2 children.
So, A's share was 1/3.
Upon his death this 1/3 share of A is succeeded to by B and the 2 children.
So, B's share will be 1/3(1/3) = 1/9.
Similarly, if there were 3 children, then B's share would be 1/16.
The above is applicable for Hindus only, and the property being situated in India.