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The couple brought their families together on Saturday for a trip to the famed Magic Castle in Los Angeles. "Since Jennifer and Ben are in it for the long run, it's just a natural step that they all spend time together with the kids," a source tells PEOPLE.
"They are not trying to rush anything, but they want all the kids to get to know each other," the insider adds. "They are making the last few days of summer as fun as they can. Soon it's back to school and work."
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Affleck, 49, and Lopez, 52, were accompanied by all five of their kids, as well as Affleck's mother Chris, for a fun family weekend. Their brood also took in a performance of Hamilton at the Hollywood Pantages Theatre on Friday.
The "Jenny from the Block" artist co-parents her twins, daughter Emme and son Max, both 13½, with ex-husband Marc Anthony, 52. Affleck shares his daughters Violet Anne, 15½, and Seraphina Rose, 12½, and son Samuel Garner, 9, with ex-wife Jennifer Garner, 49.
Affleck also gave Violet a driving lesson during their family weekend.
With help from Emme, Lopez picked out some jewelry for Violet and Seraphina last weekend, which she planned to gift them during their dad's 49th birthday gathering.
The couple, who recently vacationed in St. Tropez for Lopez's 52nd birthday, has been getting to know each other's kids as Lopez plots a move from Miami to Los Angeles, where Affleck is based.
Emme and Max are "onboard with starting fresh in Los Angeles," an insider previously told PEOPLE. "They are slowly getting to know Ben," the source added. "Everything seems to be running smoothly. It's very obvious that Jennifer is serious about Ben. She hasn't looked this happy for a long time."
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Following their respective splits from Alex Rodriguez, 46, and Ana de Armas, 33, Lopez and Affleck rekindled their romance in late April. They originally began dating in July 2002 after meeting on the set of their movie Gigli. They got engaged that November before postponing their September 2003 wedding just days before the original date, and ultimately called off their engagement in January 2004.
A source told PEOPLE in May that their relationship is different this time around. "Time has passed, and they are each in a different place with children," the insider said.