1) Biden's son was not under investigation. Mykola Zlochevsky, who founded Burisma holdings, a company that Hunter Biden sat on the board of, was under investigation.
2) The U.K. had sought to have the prosecutor in the case, Viktor Shokin removed. Vitaly Kasko, a deputy prosecutor in the case, has stated that although the U.S., just like the U.K., wanted Shokin fired, they did not pressure anyone to drop the inquiries... just dump Shokin, the corrupt prosecutor.
3) It absolutely was digging up dirt on a political rival. It is either naive or dumb to think that Trump's interest in this, wasn't purely politically motivated. In other words, a witch hunt.