You can use the mtchideinmaintoc environment to hide information in the main ToC:
\documentclass[a4paper,oneside]{scrbook}
\usepackage{minitoc}
\setcounter{tocdepth}{0}
\begin{document}
\doparttoc
\tableofcontents
\part{Part 1}
\parttoc
\begin{mtchideinmaintoc}
\addstarredchapter{Chapter}
\chapter*{Chapter}
\end{mtchideinmaintoc}
\chapter{Chapter 1}
\chapter{Chapter 2}
\part{Part 2}
\parttoc
\begin{mtchideinmaintoc}
\addstarredchapter{Chapter}
\chapter*{Chapter}
\end{mtchideinmaintoc}
\chapter{Chapter 3}
\chapter{Chapter 4}
\end{document}
The main ToC:

An image of one of the partial ToCs:

One can define a command to do this in a more succinct way:
\documentclass[a4paper,oneside]{scrbook}
\usepackage{minitoc}
\setcounter{tocdepth}{0}
\newcommand\Mychapter[1]{%
\begin{mtchideinmaintoc}
\addstarredchapter{#1}
\chapter*{#1}
\end{mtchideinmaintoc}}
\begin{document}
\doparttoc
\tableofcontents
\part{Part 1}
\parttoc
\Mychapter{Chapter}
\chapter{Chapter 1}
\chapter{Chapter 2}
\part{Part 2}
\parttoc
\Mychapter{Chapter}
\chapter{Chapter 3}
\chapter{Chapter 4}
\end{document}
Of course, one could also make this redefinition for the internal command \@schapter (in charge of starred chapters); but this might have undesired side-effects since internally \chapter* is used for several document units (ToC, LoF, LoT, bibliographies, indexes):
\documentclass[a4paper,oneside]{scrbook}
\usepackage{minitoc}
\setcounter{tocdepth}{0}
\makeatletter
\renewcommand*{\@schapter}[1]{%
\begin{mtchideinmaintoc}
\addstarredchapter{#1}
\if@twocolumn
\if@at@twocolumn
\@makeschapterhead{#1}%
\else
\@topnewpage[\@makeschapterhead{#1}]%
\fi
\else
\@makeschapterhead{#1}%
\@afterheading
\fi
\end{mtchideinmaintoc}
}
\makeatother
\begin{document}
\doparttoc
\tableofcontents
\part{Part 1}
\parttoc
\chapter*{Chapter}
\chapter{Chapter 1}
\chapter{Chapter 2}
\part{Part 2}
\parttoc
\chapter*{Chapter}
\chapter{Chapter 3}
\chapter{Chapter 4}
\end{document}