Package hyperref needs unique anchor names. The anchor names are mostly using the counter values. To support non-unique counter values, package hyperref uses a companion form of the counter theHcounter, which is not used for typesetting but for the anchor names. Thus you would need, e.g.:
\renewcommand*{\theHchapter}{\theHpart.\thechapter).
Package hyperref adds support for \@addtoreset or \counterwithin, but this will only work, when they are used after hyperref is loaded.
Example:
\documentclass{book}
\usepackage{chngcntr}
\usepackage{hyperref}
\counterwithin*{chapter}{part}
\begin{document}
\tableofcontents
\part{One}\label{part:one}
\chapter{First}\label{chapter:first}
\part{Two}\label{part:two}
\chapter{Second}\label{chapter:second}
\end{document}