Loki was angry, which was to be expected. For his part, Odin kept his emotions in check. He was tired, so very tired and so very sad. Being a ruler never got any easier.
"No, not all of it. I knew they would die, but I did not know the details of what would bring it about. You think it pleased me to allow my own son's deaths? My sons, Loki. I know how you felt about Hodr, but he was MY SON." Perhaps he wasn't the son Baldr was, or Thor, or an other number of sons Odin had sired. That did not mean he had no feelings for the boy. As for Frigg's attitude, Baldr was her first born, and the light of her world. He had no knowledge to what extent her attitudes would affect the two boys.
"Frigg tried to stop it. All it did was provide an easier path to the same outcome. Your slate is not clean in this, either." Loki could have ignored Hodr's request. He didn't have to go find out about the mistletoe. As Loki said, he chose to assist Odin's dark son. Yet it was as it had been foretold. "Proof that no matter what we might do, nothing can change what must be."
Odin waved a hand at Loki's outburst about them all hating him. What could Odin say to that? For the Trickster spoke the truth; most of Asgard did indeed look down upon the Fire Giant.
"I'm sorry, Loki." Sorry for what? For bringing his friend here? For using him as he had time and again to further Asgard and his own personal gains? For allowing people to feel how they would feel? No one can dictate another's emotions.
"I could stand here now, protect you and turn away any who might venture near, but you and I both know it will make little difference." Unless Odin was to stand guard around the clock, without sleep, there was no way of stopping what would come. "They would find a way." Not to mention that he would lose respect as their ruler. Loki had gone too far, and many would want vengeance. To allow him to go unpunished would not serve the peace of Asgard.
So Loki would be caught, and his wife and children could move elsewhere. They, at least, would be safe, unlike his own children. Odin had sacrificed more than Loki would ever have to face, by choice or otherwise, by his own actions or another's.