"This is so ridiculous," Trump, 63, tells PEOPLE. "There was a report in the Palm Beach Daily News that Melania and I are having problems, and it is 100-percent false, as I told them."
"The truth is," he says, "our 5-year-old son Barron is in school [in New York] on Fridays until 5 p.m. and we don't want to take him out to fly down to Palm Beach. So I have come alone. I left really early this past weekend because of the snowstorms."
Trump, who stars on NBC's Celebrity Apprentice, says that Melania, 39, is a good wife and mom, and these rumblings, started by bored Palm Beach socialites, are totally untrue. For the record, the Palm Beach Daily News merely inquired of Trump as to the status of his marriage.
"Melania used to come with me to Palm Beach every weekend, but now that we have a young son, his school comes first," Trump tells PEOPLE.
This weekend, however, there will be special plans for Valentine's Day. "I am bringing Melania to Mar-a-Lago and plan to take her to the annual Palm Beach Heart Ball on Saturday night," says Trump. "She is the co-chairwoman! All is well."