Upon the incapacity of the President the Vice President becomes Acting President (unlike the death or resignation of the President, when the Vice President becomes President). There is a procedure for the President to seek to regain power, in which case Congress would adjudicate any dispute.
Admittedly, the Vice President Elect is a fruitcake who believes it is possible to turn gay people straight through the medium of electrocution, but it is submitted that he is more likely to consider himself bound by constitutional norms than Trump.