Let us break down the given information step-by-step to determine the relationship between $Q$ and $S$:

Step 1: Determine the genders of $S$ and $R$

• We are given that $S$ is the mother of $T$. This means $S$ is a female.
• We are also given that $S$ is $R$'s spouse. Since $S$ is a female, her spouse $R$ must be a male (husband of $S$).

Step 2: Determine the gender of $Q$

• We are given that $Q$ and $R$ are the children of $P$.
• The first statement says $P$ has exactly one son and one daughter.
• Since we already established that $R$ is a male, $R$ is the son of $P$.
• Therefore, the other child, $Q$, must be the daughter of $P$. This makes $Q$ a female and the sister of $R$.

Step 3: Find the relationship between $Q$ and $S$

• $Q$ is the sister of $R$.
• $R$ is the husband of $S$.
• Hence, $Q$ is the sister of the husband of $S$ (which also means $Q$ is the sister-in-law of $S$).

Comparing this conclusion with the given options, Option D perfectly matches our deduction.