Nuking them wouldn’t weaken us at all except morally. You make comic book style arguments, as if our moral uprightness is our source of strength in war, even though we’ve compromised our values in every hard war we’ve ever fought and survived the experience(and lionized the leaders who led us down that path).
A student of history would recognize these arguments as straight from the 1920s. And we all know what happened not too long after, the most savage war in human history. We are headed inexorably down that path if ISIS succeeds in establishing their caliphate.