I wouldn’t worry much about her running for any American office if the taxman is correct:
“Once you relinquish your citizenship voluntarily it is extremely difficult, if not impossible, to get it back later. With renouncing the US citizenship you also give up your right to work in the US and must apply for a visa or Green Card like any other immigrant.”
https://onlinetaxman.com/common-myths-us-citizenship-renunciation/
Pretty sure She hasnt renounced her citizenship. She is still not a UK citizen.
Archie is a dual citizen. Lord help us, Clinton and crew could be planning on him running for POTUS one day.