Step 1: Use given relations.
- $T$ is the brother of $U$.
- $T$ is married to $P$.
- $R$ has only two children: $P$ and $S$ (both daughters).
- $W$ is the mother of $Q$; $W$ is married to $X$ (so $X$ is father of $Q$).
Step 2: Identify sister\textendash in\textendash law of $U$.
By definition, a sister-in-law of $U$ can be (i) the wife of $U$'s brother, or (ii) the sister of $U$'s spouse.
Here, $U$'s brother is $T$, and $T$'s wife is $P$.
$\Rightarrow$ $P$ is the sister-in-law of $U$.
\[
\boxed{P}
\]