They were never friendly, but remained on 'Christmas card' terms. And yes, their families did meet, but Harry and Dudley hardly spoke and Harry's children dreaded the visits.
From an interview with JKR:
A couple of people have told me that they hoped to see Dudley at King’s Cross in the Epilogue, accompanying a wizarding child. I must admit that it did occur to me to do that very thing, but a short period of reflection convinced me that any latent wizarding genes would never survive contact with Uncle Vernon’s DNA, so I didn’t do it.
However, I know that after Dudley’s brave attempt at reconciliation at the start of Deathly Hallows, the two cousins would have remained on ‘Christmas Card’ terms for the rest of their lives, and that Harry would have taken his family to visit Dudley’s when they were in the neighbourhood (occasions dreaded by James, Albus and Lily).
And another one:
Harry and Dudley would still see each other enough to be on Christmas-card terms, but they would visit more out of a sense of duty and sit in silence so that their children could see their cousins.