Aligning inside tabular environment, specific cell

You can use \multicolumn{1}{l}{<content>} for to_the_left to switch the cell alignment just for this cell. If you want to have a vertical line you need to use l| instead, otherwise the line is missing for this cell.

\documentclass{article}
\begin{document}
\begin{tabular}{|r|r|}
   \hline
   111111 & 222222 \\
   \hline
   right & \multicolumn{1}{l|}{left} \\
   \hline
   1 & 2 \\
   \hline
\end{tabular}
\end{document}

There is a "solution" that avoids \multicolumn{1}{l}{...} but it's really a hack:

right & left\hfill\vadjust{} \\

The \hfill alone won't do, because LaTeX works hard to remove all space from the end part of a cell. Instead of \vadjust{} also \penalty0 or \nobreak can be used.

A \multicolumn{1}{l}{...} is, probably, more visible and easier to change in case it's not needed any more.