I don't think that the scenario where Putin detonates a nuclear weapon as a demonstration, or within the border of Ukraine would cause the US/UK/France to detonate one of their nuclear weapons to prove they are serious. Only an attack on a Nato country, with casualties, would bring a nuclear response.
I really, really hope so. if NATO used a nuke of its own in response to one in Ukraine, this just confirms Putin's rhetoric that NATO isn't just a defense alliance, that we would launch outside of Article 5. that's the "existential threat."
I just wish we were less hawkish, because it seems like we're playing with fire by supplying arms to Ukraine.