Using multiple math fonts causes characters and spacing problems with delimiters

Question

I am using Pagella as my main math font but MnSymbol for the \mathcal font and this has strange interactions.

The following code

\documentclass{article}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmathfont{texgyrepagella-math.otf}
\setmathfont[range={cal}]{MnSymbol}
\begin{document}
 $\big||a| - |b|\big|\leq|a-b|$
\end{document}

compiles to

In relation with the answer that worked well for my previous problem with the range feature of unicode-math, I tried

\documentclass{article}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmathfont{texgyrepagella-math.otf}
\setmathfont[range={cal}]{MnSymbol}
\setmathfont[range={up,it,tt,bb,frak, scr}]{texgyrepagella-math.otf}  %% NEW
\begin{document}
 $\big||a| - |b|\big|\leq|a-b|$
\end{document}

which improves things but leaves some ununderstandable space :

I would like this inequation to look like this (achieved by not using MnSymbol at all, but I want it for my mathcal !)

Note : in this example, replacing the explicit \big by \left and \right gives a correct output, even without the workaround. But this \left. \frac12 \right) gives the same strange glyph for the left delimiter (although the workaround eliminates this one !).

Answer 1

Use \setmathfontface to setup up a \mathXX font:

\documentclass{article}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmathfont{texgyrepagella-math.otf}
\setmathfontface\mathcal{MnSymbol}[]

\begin{document}
 $\mathcal{A} \big||a| - |b|\big|\leq|a-b|$
\end{document}