How to insert a page break in a minitoc but not in toc?

An easy way of managing the ToC entries is to highjack one that you'll probably never use. That way the process behind the scenes remains the same, especially when dealing with minitoc. So, below I take over how starparagraphs (stemming from paragraph*) is handled:

documentclass{memoir}
usepackage[T1]{fontenc}
usepackage[utf8]{inputenc}
usepackage{minitoc,etoolbox}

usepackage{xr-hyper}
usepackage{varioref}
usepackage{hyperref}
usepackage{cleveref}

setsecnumdepth{subsection} % numbering of subsection if memoir document
setcounter{tocdepth}{1}
setcounter{minitocdepth}{2}

newcommand{addtominicontents}[1]{%
  addcontentsline{toc}{starparagraph}{#1}%
}
newififmaintoc% Used to see whether we're setting tableofcontents or minitoc
AtBeginDocument{%
  letoldtableofcontentstableofcontents
  RenewDocumentCommand{tableofcontents}{ s }{%
    maintoctrue% In the main ToC
    IfBooleanTF{#1}
      {oldtableofcontents*}
      {oldtableofcontents}%
    maintocfalse% Outside of the main ToC
  }%
}
letoldcontentslinecontentsline
renewcommand{contentsline}[4]{%
  ifnumpdfstrcmp{#1}{starparagraph}=0% If we're processing a starparagraph
    ifmaintocelse% In the main ToC, do nothing, otherwise
      #2% Set it as-is
    fi
  else% We're not processing a starparagraph, so execute the regular contentsline process
    oldcontentsline{#1}{#2}{#3}{#4}%
  fi
}

dominitoc

begin{document}

tableofcontents
adjustmtc

chapter{1}
minitoc

section{1a}
Hello
subsection{1aa}
blabla

addtominicontents{protectvfillprotectpagebreak}

subsection{1ab}
blabla
section{1b}

end{document}

The approach is to write whatever you want to the regular (main) ToC under the guise of being a startparagraph. Then, process starparagraph entries in an as-is way, rather than setting them in the usual ToC manner (with a clickable hyperlink, a leader and page number). Since the ToC-related hyperlinking is broken into parts (to capture the destination of the link and set it across the sectional unit title), it's easier to condition at the start of contentsline whether we're dealing with a starparagraph or not. Then, within the true branch, we condition on whether we're in the main ToC or not, just to make sure we completely ignore the entry in the former case, but set it as-is in the latter.

Here is the default (main) ToC:

And here is the mini-ToC for Chapter 1, broken in two:

If you're not running a current/up-to-date LaTeX, you may have to add usepackage{xparse} to your preamble before being able to use RenewDocumentCommand.