It's important to remember is that the replacement portion of a  s/search/replace/ substitution (the part between the second  // pair) exactly obeys the single- or double-quote interpolation rules of any single- or double-quoted literal. The substitution above could be re-written as
    s{search}"replace"
or, if no interpolation was wanted, as
    s{search}'replace'
instead.

String interpolation in Perl does not nest. (A Perl string is not an AST macro.) If I start with a string
    my $s = 'fee \n fie $foo fum';
(again, single-quoting completely defeats interpolation), I get a string that is literally
    fee \n fie $foo fum
If I then intepolate this string into another string, the second string is not re-scanned after interpolation to handle anything that looks like it might possibly be further interpolated.

c:\@Work\Perl>perl -wMstrict -le
"my $s = 'fee \n fie $foo fum';
 print qq{'$s'};
 ;;
 my $t = qq{zit $s zot};
 print qq{'$t'};
"
'fee \n fie $foo fum'
'zit fee \n fie $foo fum zot'
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You may be looking for some sort of text templating system, e.g., Text::Template. The  s///ee 'trick' shown by LanX above works, but lacks generality.