It's a tough one. Click and treats is an excellent idea, except that it needs to be simultaneous, and if he first dashes under the bed, and you have to go and hunt for him to get him out or reassure him, the moment has already passed. Unless perhaps you could have your cat, safely in the room where he goes to hide, with the door closed, feeling safe, and THEN have someone ring the bell and do your click and treat. Worth a try!
Perhaps you could counter-condition him by you yourself ringing the doorbell when you come home. You could also try something like changing the doorbell chime. Play it by ear though, I mean if it really causes her a ton of trauma then you might have to re-think it.
When/if you could ever get him face-to-face with the child, of course then, it's treats and his favorite form of play. It's got to be a "jackpot" type of moment.
I have a scardy-cat too, Neytiri, but maybe not quite as scared as yours. I have a friend who comes over now and again, and everytime she does, Neytiri runs and hides, like you describe. In her case it was running up the stairs and hiding out in my bedroom. My friend desperately wanted to be friends with Neytiri, and Neytiri is such a cuddly, affectionate cat that I knew that if I could ever "help things along" that it would be wonderful for both of them. I first tried things like carrying Neytiri downstairs, slowly, giving her lots of reassurance. That just got me scratched up, and Neytiri traumatized. Bad idea. After a few visits, where nothing traumatic happened for Neytiri, she started getting a little bit curious, she would come out of the bedroom and hang out at the top of the stairs. My friend would come and quietly sit at the bottom of the stairs, tossing and dragging Neytiri's favorite toy: a long strand of kitted wool (ironically one that she made her). The first visit: nothing, Neytiri just stared down suspiciously at her, and any movement towards her caused her to take off. Next visit, Neytiri same thing, except she ventured down a few steps, nervously. Eventually we got her so that she would bat at the toy a little bit, keeping a few steps between her and my friend. The last visit, she played more and was feeling more confident, and when my friend went and sat on the couch, Neytiri eventually followed her down there. She was still really nervous, and looking for reasons to bolt back upstairs, but my friend kept still, let Neytiri come to her, and when she did: treats, and soft voice encouragement, Eventually Neytiri decided that she was ok, and started rubbing up against her and accepting pets... then more pets, then lots of pets, then sitting in her lap, and demanding pets
It worked out really well eventually, but it sure was slow progress getting there. At various points my friend actually got quite discouraged thinking that "Neytiri hated her" etc. It went from "not terrified" to "best friends" pretty quickly, the hard part was going from "terrified" to "not terrified".