Make titlepage one-sided (centered) while all other pages are two-sided

Please provide full examples.

Do you use the package geometry?

Here a solution with KOMA:

\documentclass[a4paper,
, 12pt
, titlepage
, toc=listofnumbered
, bibliography=totoc
,  demo
]{scrbook}
\usepackage{graphicx}
\newenvironment{tpage}[3]{%
\KOMAoptions{twoside = false}
  \begin{titlepage}
    \title{#2}
    \subtitle{#3}
    \date{City, den \today}
    \author{#1}

    \titlehead {
      \begin{minipage}[b]{0.6\textwidth}
        Institution\\
      \end{minipage}
      \begin{minipage}[b]{0.4\textwidth}
        \begin{flushright}
          \includegraphics[scale=0.5]{somelogo.pdf}
        \end{flushright}
      \end{minipage}
      \hrule
    }

    \maketitle
  \end{titlepage}
\KOMAoptions{twoside}
}{}

\usepackage{lipsum,showframe}
\begin{document}

\tpage{Author}{TITLE}{SUBTITLE}
\lipsum

\end{document}

By using the fullsizetitle of the titlepage package of KOMA-Script you could remove all margins and produce a symmetric layout, by \addmargin or \centering for example.

Starting with my answer in Remove margins for title page, here's a simple example with a symmetric title page and asymmetric following pages:

\documentclass{scrbook}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{titlepage}
\title{Test}
\author{Stefan}
\begin{document}
\begin{fullsizetitle}
\centering
\vspace*{3cm}
\Huge Title\par
\bigskip
\Large Author\par
\today\par
\end{fullsizetitle}
\blindtext[3]
\end{document}