For certain conservatives, it always boils down to "But, Hillary!"
IIRC, when President Obama came into office, numerous Democrats wanted George W Bush and his top associates investigated for war crimes. Obama turned them down flat.
I'll say this much for your idea: If President Trump gets desperate enough and orders Attorney General Sessions to prosecute Hillary Clinton, every Trump supporter would stand up and salute, and a Republican Congress would have a hard time finding the legislators to continue investigating Russian attempts to interfere with the election. People would be so distracted, the Republicans could pass anything they wanted to.
But it smacks of despotism, of banana republic dictators.
And, think about this:
If a Democrat wins the 2020 presidential election, and ordered President Trump be investigated for obstruction of justice, graft, violating the emoluments clause, etc., Trump supporters wouldn't have a leg to stand on. All their howling would be so much hot air.