Yeah, if you have a Conquistador, just get access from Ming for a short while, if you can.
Or, if you don't mind playing the waiting game, you could see if their isolated province might revolt and defect to MNG, given enough war exhaustion and support for rebels. The AI tends to use harsh treatment and buys down war exhaustion aggressively, but waiting it out might make more sense than engaging Ming in a war.
Or take them out in two or three bites, taking all but the current capital in this war, the capital in the next. MNG will probably get around to the isolated province for you. Still means a bit of a delay, of course, and means you can't release them as a vassal, if that was your plan.
But attacking MNG for the one province just doesn't seem like something you really want to do, unless you were ready to attack them, anyway.