I don’t think that. I think they want to protect their borders like US would, if Russia moved into Mexico and started pointing missiles at America.
Then, as I have said many times before, let Putin agree to withdraw from Ukraine in exchange for a treaty of Ukrainian neutrality. He will not do it. Whether you want to accept it or not, Putin has for years stated that he does not view Ukraine as a real country, that it is an invention of the anti-Russian west, and that recognizing Ukrainian independence was Lenin’s mistake. Take him at his word. He did not invade Ukraine for fear of NATO, but because he thought he could reunite Ukraine to mother Russia. He has said as much.
I should also point out, in the case of your scenario with Mexico, we would only be seeking to expel the Russians, not annexing Mexico.