If Trump fires Rosenstein he can replace him with someone loyal to him to help stymie the investigation. No, Mr Mueller, you can't interview him, no Mr. Mueller, there will be no more funding. Comes out and states this investigation is going nowhere from time to time. Or at worst his new appointee fires Mueller and shuts down the investigation.
If Trump fired Rosenstein and replaces him with a lackey that willingly fires Mueller and shuts down the investigation? What happens?
IMO..As it stands now, in this political climate, he gets away with it. The House of Representatives will do nothing; Paul Ryan will probably say he finds it concerning, He is just new at this presidentin thing, but the odds he'll take the only action he possibly could - impeachment - are zero. The Senate will do nothing. There is no one in the Executive Branch who will do anything. The only brake on the President is Congress, and they'll do nothing. The GOP has successfully smeared the FBI and Department of Justice enough that the Trump base will totally, unequivocally support the firings. The Gowdys and McCains in the GOP are outnumbered twenty to one. Trump base are not a majority of the US populace, but they are enough to prevent Republicans in Congress from acting.
So once Mueller is fired, it's likely over. There will be no investigation, and there is no legal means to stop him that anyone will take, because only Paul Ryan can do that. And I'm assuming he won't. It's amazing the guy can even stand, missing that backbone of his. Come November, even if the Democratic Party wins the House. They cannot get the 67 seats in the Senate necessary to convict, and the investigation will have long since stopped, so people will be accepting the new normal.