At the end of the story, has Gulliver reconciled himself fully with family?

No, if anything it is worse. Gulliver has learned much on his journey. He has become enamoured with Houyhnhnms and really does not wish to leave them. Finally back in England, Gulliver's family is thrilled to see him alive, but Gulliver thinks of them only as Yahoos and cannot stand to be near them. He buys two horses and spends at least four hours a day in the stables conversing with them.