Seven people of a family $P1,P2,P3,P4,P5,P6$ and $P7$ go on a picnic in a sports utility vehicle. $P4$ is the sister of $P7$, $P2$ is the mother of $P6$'s wife. $P6$ is the son-in-law of $P3$. $P5$ and $P7$ are the grandsons of $P3$. Two people in that group of $7$ are fathers; two are brothers; two are mothers; and one is a sister. What is the relationship between $P1$ and $P4$?

$P6$ is the son-in-law of $P3$.

So, $P6$ is married to the daughter of $P3$.

Also, $P2$ is the mother of $P6$'s wife.

So, $P6$'s wife is the daughter of $P2$ and $P3$.

Hence, $P1$ can be taken as the wife of $P6$.

Now, $P5$ and $P7$ are the grandsons of $P3$.

Also, $P4$ is the sister of $P7$.

So, $P4$ is the daughter of $P1$ and $P6$.

Therefore, the relationship between $P1$ and $P4$ is Mother-Daughter.