Russia would not tolerant international military intervention in Chechnya anymore than the United States would a military intervention into Mexico. Chechnya is on the border with Russia, it's literally its backyard, so there's no logical reason it would not object to such an aggressive move. The United States is no different.
Russia would not tolerate any foreign military intervention in Chechnya. Russia is still a World Superpower, and if one of their satellites get any intervention from a foreign military, would make them appear weak. If Russia believes there need to be an intervention there, Russia will be able to take care of it themselves.