The same way they did in 2014. Don't worry, the US is very used to this (and this is just from a NATOpedia article).

In this scenario, by assuring the coup plotters that the U.S. will keep funding the war as long as they keep fighting it, as opposed to cutting bait with the coup as an excuse. The coup plotters would then accuse the deposed government of treasonously planning a surrender (a mischaracterization, but that's par for the course) and portray themselves as acting in the national interest. They then keep the status quo of the war, with just a change in management. This would all fit neatly with the anti-Russia/pro-U.S. propaganda Ukraine has been subjected to. Any Russian objection would be written off as lies.

If Russia tried to support a coup government, that government would be branded as treasonous even if they sought to act in the best interest of the Ukrainian people. The U.S. would immediately seek to discredit and destabilize the coup government, and a lot of Ukrainians would listen as they're fighting a war with Russia.

Zelensky just removed Zaluzhny from heading the military because Zaluzhny was getting too popular and becoming a political threat. Important to point out that Zelensky has called off the elections that should be happening right now and that there's growing dissent for his administration due to how poorly the war is going. Also worth pointing out that Zaluzhny has ties to the far right militias of the Ukrainian armed forces and flaunted this fact when Zelensky first tried to have him removed. It would be very easy for NATO to back Zaluzhny and his right wing thugs (the same ones that took part in the maidan coup) against Zelensky if Zelensky breaks with the West's wishes. US intelligence agencies are very good at pulling at threads of existing dissent to create chaos and oust difficult political leaders