There are theories that Wooly is Amanda's father or something like that, but I think it's someone else. Amanda clearly doesn't like him, and he's not as kind as he might seem (for example, the moment from the second part where he makes Riley tell his story that angers Amanda, knowing that the monster will definitely attack Riley in this case)
What if Woolie used to work in Hameln, which is why Amanda still doesn't like him? After all, he was involved in what happened to her
(sry if this writen poorli, my english is bad)