How can I get extra subtitles for chapter titles that also appear in the ToC?

This simple solution should work for you. It is not formatted as you wished, but I really cannot imagine a ToC with subtitles below some title there.

\documentclass{report}

\newcommand\Chapter[2]{
  \chapter[#1: {\itshape#2}]{#1\\[2ex]\Large\itshape#2}
}

\begin{document}

\tableofcontents

\Chapter{My chapter}{Nice subtitle}

Lorem ipsum ...

\chapter{Another chapter}

Lorem ipsum ...

\end{document}

Alternative definition of \Chapter to have the subtitle below the title in ToC:

\newcommand\Chapter[2]{\chapter
  [#1\hfil\hbox{}\protect\linebreak{\itshape#2}]%
  {#1\\[2ex]\Large\itshape#2}%
}