Replace characters in string based on preceding and following character

Here is a solution using LaTeX packages (works with l3regex, xparse and the expl3 bundle from 2011-10-09 onwards).

\RequirePackage{l3regex,xparse}
\ExplSyntaxOn
\tl_new:N \l_removedots_tl
\tl_new:N \l_removedots_str
\DeclareDocumentCommand{\removedots}{+v}
  {
    % Store the verbatim argument into a macro.
    \str_set:Nn \l_removedots_str {#1}

    % Remove all dots followed by a non-digit.
    \regex_replace_all:nnN { \.(\D) } { \1 } \l_removedots_str

    % Replace "non-digit--dot--digit" by "non-digit--space-digit".
    \regex_replace_all:nnN { (\D)\.(\d) } { \1\ \2 } \l_removedots_str

    % Re-tokenize the result, storing it into `\l_removedots_tl`
    \tl_set_rescan:Nno \l_removedots_tl
      {
        \int_set:Nn \tex_newlinechar:D { `\^^M }
        \int_set:Nn \tex_endlinechar:D { `\^^M }
      }
      \l_removedots_str

    % Then simply typeset that, but you could do other things to it.
    \tl_use:N \l_removedots_tl
  }
\ExplSyntaxOff


\documentclass{article}
\begin{document}

\removedots |Unicom Computer Corp. (in re), 13 F.3d 321, 30 Collier Bankr. Cas. 2d 655, 25 Bankr. Ct. Dec. 152 (9th Cir. 1994)

Personal Property Security Act (P.E.I.), R.S.P.E.I. 1988, c. P-3.1|

\end{document}

Under the hood, this is doing a lot of work, because TeX is not well suited to regular expression parsing. It will be difficult to do the same directly in TeX primitives.

With a simple loop, xstring is also able to do such things:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{xstring}
\def\removedot#1{%
    \def\citation{#1}%
    \loop
        \StrPosition\citation.[\dotpos]%
        \ifnum\dotpos>0
        \StrMid\citation1{\number\numexpr\dotpos-1}%
        \StrChar\citation{\number\numexpr\dotpos-1}[\antechar]%
        \StrChar\citation{\number\numexpr\dotpos+1}[\postchar]%
        \antechar
        \IfInteger\postchar{\IfInteger\antechar.{\unless\ifx\postchar\space\space\fi}}{}%
        \postchar
        \StrGobbleLeft\citation{\number\numexpr\dotpos+1}[\citation]%
    \repeat
    \citation
}
\begin{document}
\removedot{Unicom Computer Corp. (in re), 13 F.3d 321, 30 Collier Bankr. Cas. 2d 655, 25 Bankr. Ct. Dec. 152 (9th Cir. 1994)\endgraf
Personal Property Security Act (P.E.I.), R.S.P.E.I. 1988, c. P-3.1}
\end{document}

EDIT: sorry for the bug. Here is a code in which the bug is fixed and the result is stored in the macro \newcitation:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{xstring}
\def\expaddtocs#1#2{%
    \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter
    #1\expandafter\expandafter\expandafter{\expandafter#1#2}}
\def\removedot#1{%
    \def\citation{#1}\def\newcitation{}%
    \loop
        \StrPosition\citation.[\dotpos]%
        \ifnum\dotpos>0
        \StrLeft\citation{\number\numexpr\dotpos-2}[\temp]\expaddtocs\newcitation\temp
        \StrGobbleLeft\citation{\number\numexpr\dotpos-2}[\citation]%
        \StrChar\citation1[\antechar]\expaddtocs\newcitation\antechar
        \StrChar\citation3[\postchar]%
        \IfInteger\postchar
            {\IfInteger\antechar{\expaddtocs\newcitation.}{\unless\ifx\postchar\space\expaddtocs\newcitation\space\fi}}
            \relax
        \StrGobbleLeft\citation2[\citation]%
    \repeat
    \expaddtocs\newcitation\citation
    \newcitation% use the \newcitation macro
}
\begin{document}
\removedot{Unicom Computer Corp. (in re), 13 F.3d 321, 30 Collier Bankr. Cas. 2d 655, 25 Bankr. Ct. Dec. 152 (9th Cir. 1994)\endgraf
Personal Property Security Act (P.E.I.), R.S.P.E.I. 1988, c. P-3.1}
\end{document}

For sure, none of the codes shown in this thread are written with pure plain-TeX macros. It would be so hard that it is much better to use a package, either latex3 parser or xstring, both written in plain-teX.