I'm happy that everything ended not so...But it could. And the matter was - YOU! He took Lucy's stick not because he wants sticks, probably he even doesn't like them, but because she receives them from you, he took it out of jealosy, food and toys received from the leader of the pack ( that is you) represent your attention. Then came another baby to claim the same, so, the competition became tougher. He tried to reassure himself that he is still your right hand by taking his old place, but the toddler threatened him again. Your dog has bit your baby in order to protect himself, but the person whom he loves punished him.
First of all, you made a mistake. Your dog was upset, when he had to bite your baby, he, probably didn't mean to, he was waiting for Lucy to come and grab it. But, this confrontation repeated the very next day. I suggest you not to allow him inside for the next month or so, he wouldn't forget it so easily. But, please, don't forget, that your dog would feel absolutely miserable, if you don't grant him your attention. The accident you described is a typical indoor accident, and it shouldn't stop your children playing with your dog outside, take them for walks.