Nonsense. Larry is a cat taken in when David Cameron is the Prime Minister, and after 5 of them got kicked out of the Cabinet Office, the Chief Mouser Larry is still there serving in the office. Larry doesn't care who's the premier are, Larry is just there, ready to lead in the time of political crisis.
Maybe she needs to tell her step kids, "when I'm in the White House, we'll get a cat" like the way the Obamas got Bo. The kids won't be there full time, but the cat could. And there's plenty of staff to help care for it.
Edit: Make that "some cats" and "care for them." Plenty of room and sofas, lots of bonded pairs of adult cats in shelters.