Inside Gwyneth Paltrow and Chris Martin's Decision to Split

04/03/2014 at 12:50 PM EDT

Gwyneth Paltrow, Chris Martin's Split: The Real Story in PEOPLE Magazine
Gwyneth Paltrow
They arrived for a weeklong stay in paradise with enough suitcases – and salad greens – to fill an SUV.

But that was just a fraction of the baggage Gwyneth Paltrow and Chris Martin brought with them when they landed on the narrow Bahamian island of Eleuthera on March 24.

One day after touching down with their kids Apple, 9, and Moses, 8, the pair announced that they were ending their 10-year marriage "with hearts full of sadness."

Toting "plenty of food and a lot of wine," says an observer, they retreated to a private home on the tiny neighboring island of Windermere.

The four-bedroom estate, which rents for $10,500 a week, is "an isolated place so they didn't have to deal" with the public fallout from the split, says a source close to Paltrow.

As for their decision to spend spring break together, "they're still a family," says the source. "Nothing will ever change that."

For much more on Gwyneth and Chris's decision to end their marriage, pick up this week's issue of PEOPLE magazine

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