Is there a way to not italicize a word in a \textit{} expression?

That's exactly what \emph does:

\documentclass{article}

\begin{document}

\emph{In the \emph{Smith} case, the Supreme Court held\dots}

\end{document}

or, if you prefer to manually control that, then you can use \textup:

\documentclass{article}

\begin{document}

\textit{In the \textup{Smith} case, the Supreme Court held\dots}

\end{document}