As you may know, the United States constitution grants a sitting President broad powers to pardon anyone accused of a federal crime. This power can even be proactive, as when President Gerald Ford granted a blanket pardon to Richard Nixon after the latter's resignation for any crimes he may have committed while in office, notwithstanding he had not yet been indicted.
So, legally, Trump would have no impediments if he wanted to pardon his children or people who worked for him.
Legal experts disagree, however, about whether Trump can pardon himself (details here). Nixon's own Justice Department, for instance, told him that he could not pardon himself while in office (details here).
The experts uniformly agree on one thing, however: Trump cannot pardon himself out of an impeachment. The constitution specifically says he can't. Congress can impeach him and remove him from office. Trump has no power to stop that.
Because many issues about pardons have never been tested in court before, there is no certainty that Trump could pardon members of his own family without legal repercussions. A highly esteemed law professor wrote in The New York Times yesterday (link here) that Trump's pardon power may not be as broad as he thinks it is, and if he attempts to use it in certain ways, that could open him up to future prosecution himself.
Trump may think that pardoning people will be a way to end the Mueller investigation. Not only will that not happen, it will guarantee that all kinds of evidence will come out.
Why? The answer is simple -- if you're pardoned, you can no longer plead the Fifth Amendment against self-incrimination (details here). So if Trump pardons his daughter and/or his son and/or his son-in-law, all of them can be forced to testify against their father, either in an impeachment proceedings or a criminal prosecution.
And if they refuse, they can be sent to jail until they testify, and Trump can't pardon them free.