The son of 21-year MLB veteran reliever Tom "Flash" Gordon, Dee recalls running around Fenway Park and hanging around the likes of Pedro Martinez and Nomar Garciaparra.
"They let me run around and be a kid," Gordon said. "It was awesome. We were mild-mannered. So we were fine. We didn't really mess with anybody or overstep our boundaries. They just kind of let us do our thing."
Now 27, Dee is having an All-Star-worthy season with the Marlins, reaching 100 hits in fewer games than any player in Marlins history.
Raised in a baseball family, Father's Day is another reminder for Dee to appreciate all he has.
Dee was born in 1988, the year his dad broke into the Majors with the Royals. When Tom joined the Red Sox for the first time in 1996, Dee was about to turn 8. His brother, Nick, a touted prospect with the Twins, was less than a year old. For years, Fenway Park was like a second home for them the next few seasons.
"My dad taught us very well how to stay out of the way," Dee said. "We just did what we needed to do. If [the Red Sox] weren't in the cages, we were in the cages. If they were on the field for early BP, we'd be running around, shagging for them. We knew how to stay out of the way.
"My brother, Nick, he was a little different. He wanted to be everywhere at every time. So I had to keep him pretty much grounded."
Dee recalls spending time with Pedro and Ramon Martinez, Garciaparra, Jose Canseco and others.
"For my sons, of course, they had the pressures of knowing that, hey, dad was a three-time All-Star, a World Series champion, and had 21 Major League seasons," Tom Gordon said in a video interview with MLB.com. "Of course, that's going to be tough shoes to follow. But I believe with the character that my kids represent, both boys. I believe in the hard work and the character that they represent. There are so many people willing to help them achieve the goals they want to achieve. Of course, I'm always there."
Dee either speaks with or texts his father every day.
One of the most special moments at a park for Dee came during his rookie season with the Dodgers. On Father's Day in 2011, Tom Gordon and the late great Tony Gwynn threw out the ceremonial first pitches to their respective sons, Dee and Tony Jr. It was a moving ceremony at Dodger Stadium.
"That meant a lot," Dee said. "That was significant. That was my first year in the Majors."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.