I'm Lucy, and I'd be happy to answer your questions today.
First, I want you to know, that if you were to circulate such a petition, I'd be one of the first to line up to sign it. So, I am 100% on your side here. However, with that said - this is how our system was set up. Anyone can run for President, as long as they meet the very basic qualifications: at least 35 years old and a natural-born citizen of the United States. There is no question that he meets those qualifications. The problem isn't that the candidate is being allowed to run - it's that the news media is giving him free coverage, 24/7 and has been for over a year. It's the millions of people who, for unfathomable reasons, support him. You can't sue the news outlets because of freedom of the press guaranteed by the First Amendment.
I don't know cause of action you'd be asserting if you wanted to sue Trump. You haven't suffered, at this point, any specific injury. There's no law that protects us from being appalled or horrified at other people's behavior. There's sadly no law that stops people from saying racist and offensive things. If he crosses the line into committing hate crimes, that's for the FBI or state and local police to investigate. He's arguably toeing the line in some of his speeches, but that's a criminal issue. And you can't sue him for defamation, because he's not hurting your reputation as an individual. (Also, I'm sorry to say, the rest of the world doesn't really have as good an opinion of America as we'd like to think. Some of the news reports aired in foreign countries about the U.S. are pretty horrifying.) To bring a lawsuit, you have to be able to state a legal wrong. And in a culture that embraces people making fools of themselves for publicity, I'm afraid I just don't see any particular cause of action that would apply. I wish I did.