Kourtney, Scott and their kids did lunch Tuesday at CRU in Nantucket, where eyewitnesses tell us they were ushered to a private room in the back of the restaurant with a nanny in tow. We're told Kourtney appeared to be in good spirits, even taking a selfie with a fan. Scott, on the other hand, was more reserved.

This is not, we repeat NOT, for 'KUWTK' content. Our family sources tell us they're on a family vacay, and Scott and Kourt have been on good terms.

This appears to be the first time Kourtney's linked up with her baby daddy since the disastrous trip in May they took -- although separately -- to Cannes.

They've been preoccupied with other significant others -- Younes Bendjima and Bella Thorne -- and we know Kourtney was pissed at Scott for his drinking and partying binge in France.

Still, the whole fam's together again. At least for today.