"For Gwen and Gavin, their boys always came first," says a source following the couple's split

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Gwen Stefani and Gavin Rossdale‘s marriage may be coming to an end, but it wasn’t an easy decision for the rocker pair.

The couple “were trying to make it work for the kids,” a Rossdale source tells PEOPLE, but their marriage struggles continued, and Stefani, 45, and Rossdale, 49, “have been living separate lives.”

While the couple is moving on (Stefani is set to return to coach on The Voice), they have both been spending time at their Beverly Hills mansion together with their three sons: Kingston, 9, Zuma, 7 this month, and Apollo, 17 months.

“It’s obvious that they are trying to keep things as normal as possible for their boys,” another source tells PEOPLE. “On the outside, their family life seems pretty normal. It doesn’t seem like their separation has affected their day-to-day life. For Gwen and Gavin, their boys always came first.”

The No Doubt and Bush singers – who were together for 20 years and married for 13 of those – announced their split Aug. 3.

“While the two of us have come to the mutual decision that we will no longer be partners in marriage, we remain partners in parenthood and are committed to jointly raising our three sons in a happy and healthy environment,” the pair told PEOPLE in a statement at the time.

Reporting by KC Baker and PERNILLA CEDENHEIM

For more on how Gwen Stefani and Gavin Rossdale are coping with their divorce, pick up the latest issue of PEOPLE