Clinton's comments, which came at the Trayvon Martin Foundation's third annual "Circle of Mothers" meeting, came a day after Trump used a speech at a National Rifle Association convention to blast Clinton as ill-prepared for the presidency and to falsely claim that Clinton "wants to abolish the Second Amendment."
The NRA endorsed Trump on Friday.
"Unlike Donald Trump, I will not pander to the gun lobby, and we will not be silenced and we will not be intimidated," Clinton said. "As long as children anywhere are being killed by gun violence, we will keep fighting for our kids, because they deserve a president who stands up for them and stands with the mothers here. Their lives are valuable."
Trump said Clinton was "heartless" for backing restrictions on gun ownership, and said he would overturn President Barack Obama's executive actions on guns and do away with gun-free zones, including in schools.
Clinton, responding to that speech, said Trump's vision "isn't just way out there, it's dangerous," and noted that while Trump wants to allow guns in schools, she believes "parents, teachers and schools should have the right to keep guns out of classrooms, just like Donald Trump does at many of his hotels, by the way."
"If you want to imagine what Trump's America will look like, picture more kids at risk of violence and bigotry," Clinton said. "Picture more anger and fear. Ask any of the mothers here tonight if they want to live in that kind of America. Enough is enough."
Saturday night, Trump tweeted that Clinton was wrong about his position on guns in classrooms.
"Crooked Hillary said that I want guns brought into the school classroom. Wrong!" he said.
And on Sunday, Trump offered a bit of a mixed message on the idea.
"I don't want to have guns in classrooms, but sometimes teachers should have guns," he told "Fox and Friends." "I am not advocating guns in classrooms ... trained teachers should have guns."
Guns are setting up to be a flash point issue in a general-election matchup between Clinton and Trump, with both candidates on near diametrically opposed positions.
After Trump on Friday accused Clinton of wanting to "abolish the Second Amendment," Clinton's campaign quickly hit Trump for "peddling falsehoods." Clinton has never taken that position, although she does support additional gun control measures.
Sabrina Fulton, Trayvon Martin's mother, invited Clinton to speak. Trayvon Martin was the 17-year-old Floridian killed in 2012 by former neighborhood watch captain George Zimmerman. Zimmerman's acquittal sparked protests across the country.
Fulton is a vocal Clinton supporter and has campaigned with her throughout the country.
"The reason why I stand with her is because she first stood for me," Fulton said. "Not only did she stand for me, she stood for the others as well."
Clinton met with dozens of mothers affected by gun violence before the speech. Afterward, she told the audience that each mother presented her with a letter about the child they lost.
"I am going to read every single word of these letters because each of the mothers is telling us something that we all need to hear, not just about their tragedies but about our country," Clinton said.
Clinton, in part because she met with the mothers early in her campaign, has made criminal justice reform and addressing gun violence a cornerstone of her campaign.
After nine people were killed last year during a church shooting in Charleston, South Carolina, Clinton called for universal background checks on gun purchases and more investment in mental health resources.
"I lived in Arkansas and I represented upstate New York. I know that gun ownership is part of the fabric of a lot of law-abiding communities," Clinton said. "I also know that we can have common-sense gun reforms that keep weapons out of the hands of criminals and the violently unstable while respecting responsible gun owners."
Clinton said on Saturday that favoring tough gun laws did not mean she was in favor of taking guns away from law-abiding owners. The Democratic candidate said the United States is "smart" and "strong" enough to protect people while respecting "the rights of responsible gun owners."