Thranduil may not have shown it much well Legolas was off on his quest with the Fellowship—he really couldn't show it; not with the eyes of his people on him—but he was worried about his son. He had had a fewe months of relief when he was staying in Lothlorien; but when Galadriel informed him that he had left along with the rest of the fellowship to finish their quest he had begun to worry again.
Because of this when a guard announced the arrival of Legolas when he had arrived in Mirkwood he told the guards to leave them be. As soon as the guards were gone though he moved over to his son and pulled him into a hug. After the death of his wife barely 200 years after Legolas' birth he didn't think he could bare to lose his son—especially not to the dark forces of Mordor which he had fought for so long to keep him away from.
"My son, I am glad you made it back home safely…"