Automatically correcting underbrace spacing

Question

I would like to define a command to automatize https://tex.stackexchange.com/a/503610/128042, since many LaTeX-users don't like the spacing of \underbrace (see using underbrace without having left( and right) scale, How to prevent an underbrace, with a subscript, from affecting the sizes of delimiters, Underbrace messing with horizontal spacing, ...)

I tried the following MWE:

\documentclass{article}
%\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{hyperref}
\DeclarePairedDelimiter{\norm}{\|}{\|_{2}}
\newcommand{\myVtoken}{}
\newcommand{\myunderbrace}[2]{%
    \renewcommand{\myVtoken}{\vphantom{\underbrace{{#1}}_{{#2}}}}%
    \vphantom{#1}\smash[b]{\underbrace{{#1}}_{\mathclap{{#2}}}}%
}

\begin{document}
I would like this to work:
\[
\norm*{\left(2,\myunderbrace{\frac{5}{3}}{\approx 1.66666667\frac{1}{1}} \right)}
\myVtoken %\vphantom{\underbrace{\frac{5}{3}}_{\approx 1.66666667\frac{1}{1}}} %with this \vphantom it would work
\]
The above formula is too close to this line, but this works fine: 
\[
\norm*{\left(2,\smash[b]{\underbrace{\frac{5}{3}}_{\mathclap{\approx 1.66666667}}} \right)}
\vphantom{\underbrace{\frac{5}{3}}_{\approx 1.66666667}}
\]
This text has the correct distance to the line above, because of the vphantom outside of the delimiters.

\end{document}

which produces:

The \renewcommand within the \newcommand seems not to work, the way I expected. I tried a bit around with \let and \def, but I have very litttle knowledge about them.

Does someone know how to redefine a command within a command properly to get the desired effect?

Or are there better solutions to get the desired result, where have an easy to use command where I don't have to copy the content of the \underbrace multiple times. I don't want to decide manually how large the delimiters should be using something like \big.

Answer 1

A simple and straightforward solution is available if one is willing to issue explicit sizing instructions, i.e., \big, \Big, \bigg, and \Bigg, rather than rely on \left and \right to size the parentheses and norm symbols.

A non-negligible advantage of the approach taken here is that low-level LaTeX equation placement parameters such as \abovedisplayskip and \abovedisplayshortskip needn't be tweaked.

\documentclass{article}
\usepackage{mathtools} % for \DeclarePairedDelimiter and \mathclap macros
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert_2}
\newcommand{\myunderbrace}[2]{\underbrace{#1}_{\mathclap{#2}}}

\begin{document}
\noindent
Some text some text some text some text some text \dots
\[
\norm[\bigg]{\Bigl( 2, \myunderbrace{\frac{5}{3}}{\approx 1.6667} \,\Bigr)}
\]
Some text some text some text some text some text \dots
\end{document}

Answer 2

Just I have, only, added after \begin{document},

        \abovedisplayskip=0.6cm
        \abovedisplayshortskip=-0.3cm
        \belowdisplayskip=0.6cm
        \belowdisplayshortskip=0.2cm

after to have modificated the parameters of the code that you can find into this link.

---

\documentclass{article}
%\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{hyperref}
\DeclarePairedDelimiter{\norm}{\|}{\|_{2}}
\newcommand{\myVtoken}{}
\newcommand{\myunderbrace}[2]{%
    \renewcommand{\myVtoken}{\vphantom{\underbrace{{#1}}_{{#2}}}}%
    \vphantom{#1}\smash[b]{\underbrace{{#1}}_{\mathclap{{#2}}}}%
}

\begin{document}
I would like this to work:
\abovedisplayskip=0.6cm
\abovedisplayshortskip=-0.3cm
\belowdisplayskip=0.6cm
\belowdisplayshortskip=0.2cm
\[
\norm*{\left(2,\myunderbrace{\frac{5}{3}}{\approx 1.66666667\frac{1}{1}} \right)}
\myVtoken %\vphantom{\underbrace{\frac{5}{3}}_{\approx 1.66666667\frac{1}{1}}} %with this \vphantom it would work
\]

The above formula is too close to this line, but this works fine: 
\[
\norm*{\left(2,\smash[b]{\underbrace{\frac{5}{3}}_{\mathclap{\approx 1.66666667}}} \right)}
\vphantom{\underbrace{\frac{5}{3}}_{\approx 1.66666667}}
\]
This text has the correct distance to the line above, because of the vphantom outside of the delimiters.

\end{document}