One of Hollywood's starriest couples also happens to be the most mysterious -- and Ryan Gosling and Eva Mendes want to keep it that way

Ryan Gosling and Eva Mendes are one of Hollywood’s most mysterious A-list couples — and they want to keep it that way.

The 37-year-old actor is back in the spotlight with his highly anticipated movie First Man opening Friday. But while he’s been busy promoting the Neil Armstrong biopic, his longtime love Mendes, 44, is unlikely to be joining him at any major appearances.

The two were first linked in September 2011 when they were spotted on a PDA-filled date at Disneyland after meeting on the set of The Place Beyond the Pines. Both refused to talk about their relationship at the time, and the couple of seven years is still exceptionally private about their love—which seems to work perfectly for them.

For more about Gosling and Mendes, pick up this week’s issue of PEOPLE, on stands Friday.

“They love and respect each other and try to give the other space to pursue what they love,” an entertainment source tells PEOPLE in the latest issue, adding that Gosling loves how “fiercely independent” Mendes is, though it can sometimes be “challenging.”

But, a Miami source adds, they spend every second they can with their two daughters — Esmeralda Amada, 4, and Amada Lee, 2.

'The Place Beyond the Pines' film premiere, New York, America - 28 Mar 2013
Credit: Dave Allocca/StarPix/REX/Shutterstock

“They are both in love with being parents, and can’t get enough of it,” the source says. “Neither wants to slow down on work interests but every day is a juggling act to be with their daughters.”

Echoes the entertainment source: “Like any couple they have disagreements. Now the children come first, and they share a love for them which neither had experienced before.”