Can protons be swapped in a chemical reaction?
Roughly speaking, no.   This would amount to nuclear fission/fusion, and is generally not considered "chemistry" in any colloquial sense of the term, but rather physics. 

In general, chemical reactions consider nuclei to be tightly bound by the strong force, and immutable over the course of the reaction.

Disclaimer: there is an ill-defined border between physics and chemistry, and so one could argue that I am wrong about this.  Indeed, alchemists had/have been trying to e.g. convert lead to gold for centuries, and this is related to the reaction that you propose.