Regular expressions are not meant to be used for escaped constructs.
I don't think it's possible to do this in any "nice" kind of way (if at all), although I'll post an edit if I figure out otherwise.
Balancing group definitions are for nested constructs. Nesting doesn't happen in strings, so balancing group definitions don't seem to even be the right tool for this.
Edit 1:
It depends on how many features you're looking for. If you simply want to match the next escaped quotation, you can use the pattern
^"([^\\\"]|\\.)*"
which, when escaped for code, turns out like
"^\"([^\\\\\\\"]|\\\\.)*\""
to match something like
"Hello! \" Hi! \" "
but as soon as you start adding more complicated requirements like Unicode escapes, it becomes a lot more tedious. Just do it by hand, it should be much simpler.
Edit 2:
If you're curious about how balancing group definitions work anyway, I recommend reading page 430 of this book (34 in pdf).