Gwyneth Paltrow and Chris Martin in Beverly Hills on Jan. 11, 2014 Credit: Colin Young-Wolff /Invision/AP

Not exactly the most carefree getaway of all time. As previously reported, Gwyneth Paltrow and estranged husband Chris Martin, along with kids Apple, 9, and Moses, 7, stole away to the Bahamas in advance of their surprising split announcement, which dropped via GOOP late Tuesday, March 25. "They left town just before releasing the statement to avoid the media frenzy," one source tells Us Weekly of the actress, 41, and Coldplay frontman, 37, who revealed that they're "consciously uncoupling" after over 10 years of marriage.

A second insider tells Us that the foursome are staying at a rented private beachfront home in Eleuthera; the private, ultra-secluded residence costs roughly $7,500 weekly. Since their arrival, Paltrow and Martin have been hanging out with the kids by the beach, and also carved out some time for horseback riding. "When only Gwyneth and Chris are together, there appears to be some tension," the insider says. "But when the kids are with them, they appear to be one big happy family with no cares in the world."

Still, "there are no signs of any PDA , holding hands, or kissing on the beach. There was definitely a noticeably intimate distance," continues the source Thankfully, the kids appeared to be "happy and playful" and seem unfazed by their parents' drama.

The couple's split announcement, of course, expressed their enduring commitment to raising Apple and Moses together: "We are, however, and always will be a family, and in many ways we are closer than we have ever been . . .We are parents first and foremost, to two incredibly wonderful children."

Indeed, the first source explains that the Oscar winner and British rocker "will try to make it as easy as possible" for the kids. "The whole plan is to do this as amicably as possible."