It is impossible to see why you are getting overprinting from your fragments, the following document produces

\documentclass{article}
\begin{document}
${^{\mathrm{I}}\dot {({I}_{\mathrm{p}} \omega_{\mathrm{p}} \hat{b}_3})}$
\end{document}
As it turns out, this is an amsmath feature (although amsmath was not mentioned in the question) Not fully tested but one possible fix is below.
I could add something like this to amsmath but it needs more testing, if you have a larger real docuemnt I'd be interested if this works
\documentclass{article}
\usepackage{amsmath}
\makeatletter
\def\mathaccentV#1#2#3#4#5{%
\ifmmode
\gdef\macc@tmp{\macc@depth\@ne}%
\setbox\z@\hbox{%
% only short circuit \mathaccentV if only one token after expansion
% not quite the right test but hard to test for only one math atom
\ifcat$\@gobble#5\@empty$\let\mathaccentV\macc@test\fi
% end of change
\let\use@mathgroup\@gobbletwo \let\select@group\@gobblethree
\frozen@everymath{}$#5$%
}%
\macc@tmp
\ifnum\macc@depth=\@ne
\global\let\macc@nucleus\@empty
\mathaccent"\accentclass@
\else
\@xp\macc@nested
\fi
#2#3#4{#5}%
\macc@nucleus
\else
\@xp\nonmatherr@\csname#1\endcsname
\fi
}
\makeatother
\begin{document}
$\dot{\hat{b}}$
${^{\mathrm{I}}\dot {({I}_{\mathrm{p}} \omega_{\mathrm{p}} \hat{b}_3})}$
\end{document}
\rmhas been deprecated for over 20 years, don't use it (especially not in math mode) – David Carlisle Nov 14 '17 at 16:44\rmhas not been defined in the latex format since 1993. It is added as a back compatibility definition byarticle.clsbut not all classes do this. for example.\mathrm{p}– David Carlisle Nov 14 '17 at 16:47