Sorry, Joseph, you’re wrong on both counts.
The VP together with a majority of the cabinet can vote to remove the president, either temporarily or permanently, and if he doesn’t object that’s it. If he objects, then it goes to Congress and if 2/3 of each house agree with the removal it stays in place, otherwise the president comes back.
And no, there is no automatic replacement of a cabinet member. The position remains vacant until the president nominates someone else, and the senate confirms that person. An acting secretary is not a cabinet member and cannot vote on removing the president.