Bash – How to use ‘*’ to capture everything with exceptions

Instead of parsing ls you should use find instead. Then you can also execute basename on each file to strip the leading directories:

find lib/ -name '*.jar' -exec basename {} \;

You can force another round of evaluation with eval, but that's not actually necessary. (And eval starts having serious problems the moment your file names contain special characters like $.) The problem isn't with globbing, but with the tilde expansion.

Globbing happens after variable expansion, if the variable is unquoted, as here^(*):

$ x="/tm*" ; echo $x
/tmp

So, in the same vein, this is similar to what you did, and works:

$ mkdir -p ~/public/foo/ ; touch ~/public/foo/x.launch
$ i="$HOME/public/*"; j="*.launch"; k="$i/$j"
$ echo $k
/home/foo/public/foo/x.launch

But with the tilde it doesn't:

$ i="~/public/*"; j="*.launch"; k="$i/$j"
$ echo $k
~/public/*/*.launch

This is clearly documented for Bash:

The order of expansions is: brace expansion; tilde expansion, parameter and variable expansion, ...

Tilde expansion happens before variable expansion so tildes inside variables are not expanded. The easy workaround is to use $HOME or the full path instead.

_{(* expanding globs from variables is usually not what you want)}

Another thing:

When you loop over the patterns, as here:

exclude="foo *bar"
for j in $exclude ; do
    ...

note that as $exclude is unquoted, it's both split, and also globbed at this point. So if the current directory contains something matching the pattern, it's expanded to that:

$ i="$HOME/public/foo"
$ exclude="*.launch"
$ touch $i/real.launch
$ for j in $exclude ; do           # split and glob, no match
    echo "$i"/$j ; done
/home/foo/public/foo/real.launch

$ touch ./hello.launch
$ for j in $exclude ; do           # split and glob, matches in current dir!
    echo "$i"/$j ; done
/home/foo/public/foo/hello.launch  # not the expected result

To work around this, use an array variable instead of a splitted string:

$ exclude=("*.launch")
$ exclude+=("something else")
$ for j in "${exclude[@]}" ; do echo "$i"/$j ; done
/home/foo/public/foo/real.launch
/home/foo/public/foo/something else

As an added bonus, array entries can also contain whitespace without issues with splitting.

Something similar could be done with find -path, if you don't mind what directory level the targeted files should be. E.g. to find any path ending in /e2e/*.js:

$ dirs="$HOME/public $HOME/private"
$ pattern="*/e2e/*.js"
$ find $dirs -path "$pattern"
/home/foo/public/one/two/three/e2e/asdf.js

We have to use $HOME instead of ~ for the same reason as before, and $dirs needs to be unquoted on the find command line so it gets split, but $pattern should be quoted so it isn't accidentally expanded by the shell.

(I think you could play with -maxdepth on GNU find to limit how deep the search goes, if you care, but that's a bit of a different issue.)