You don't say what interior/exterior walls are made of, or what
obstructions (other than sinks) make interior access- which would be
the normal way- more difficult. Either way, you're going to have to
open up wall and fix leak, then repair wall. Consider how laborious
that exterior wall repair may be before going that route. Is it a nice
tile job inside? I could see why that might give you pause. Ask
yourself why this leak occurred- is it possible sinks shifted due to
inadequate support? Are pipes well braced, so thst joints are
protected from movement? Just things to consider, so you only need to
do this once. Do you have kids? I had mine once cause a leak due to
poorly braced exterior vent- which was a perfect target for their
sticks/baseball bats. Sounds like that backwash drain could be
something yours might fool with.