The problem for NATO with a tactical nuke used inside Ukraine, if that were to happen, is that Ukraine is not part of NATO. Moreover, Putin would probably tell lies - either denying the fact, or claiming that NATO has smuggled in the nuke and detonated it in order to blacken Russia's name.
It's hard to know, but my guess is that NATO would not respond militarily by sending forces into Ukraine - because WWWIII would likely be the result. I hope this guess is correct.
An attack on a NATO member is a whole different kettle of fish.