Sounds like male aggressive playing to me. I have three cats who do this flying leap thing. Two of them take a running leap from the ground to my neck and seem to be able to balance themselves so they ca hold on for a few seconds just by curling their forepaws. At that point, one of them butts me on the neck and drops off -- still no claws. The butting is a sign of loving acceptance -- a bit startling the first time a cat does that to you... The other, a very large and heavy male, wraps his forelegs around my neck and butts continuously, purring, for up to 5 or 10 minutes. When I am sitting, this does not present any hardship, because his hind legs can gain stability in my lap and I can support his weight easily. But when I am standing, I have learned to raise my arms to give these attack cats hind-end support so they don't slip and accidentally claw out my carotid artery going down. I have identified the behavior of both cats as I-love-you expressions, and stopped trying to make them stop it.
The other cat is my three-legged wonder. He is still quite small and still has trouble balancing without clawing. I try to anticipate when he will jump and am ready with my hands to support him. His single foreleg is not strong enough yet to give him support without claws. We are having a rather painful time of it, but he is gradually understanding that I will automatically try to keep him from falling backwards once he has jumped. He is also very cooperative when I disengage his claws from my shoulder.
So my tack is, instead of trying negative discipline like water (you may give the cat a terror of being bathed, and you might need to use water on him at some point to save his life) and clackers, I first try (and try again) some kind of positive interaction, since I do not make the mistake of thinking that he wants to hurt me. This is my automatic response to all cat behavior now that I have lived in the middle of so many cats -- household and strays alike. But I confess if a perfectly strange cat leapt at me like that, I would instinctively put up my arms to defend myself.
I think your play sessions with the cat should include your daughter. She is the one who is becoming shy of the cat and she needs some supervised play time with him to restore her confidence. She also needs to understand why cats use their claws, and not to get too fussed if she gets scratched. You might also teach her to avert her face as soon as she sees the cat in the air, since, I can personally attest, a clawed face is rather painful, not to mention the possibility of the cat hitting one of her eyes by accident.
Castration doesn't always completely deaden a male's aggressive tendencies, but while my males may fight among themselves (or have lengthy growling sessions), they have never, since they were past 6 or 7 months, scratched me with intention. They have given me so much confidence that I now feel quite comfortable breaking up the more serious cat fights by either picking one up and carrying it off to another part of the room, or doing my hooding act -- that is, putting my hands between their faces (palms toward their noses) so they can't look each other in the eyes, and alternately massaging their temples and necks and shielding their eyes in a kind of rhythmic way until they become less taunt and their body language indicates they are ready to disengage. I then pick up the most aggressive and walk off cuddling him and cooing until his body is relaxed.
I don't really recommend this technique to most people, because you have to be absolutely unafraid of being scratched. It is the fear of being scratched that often increases the alarm and aggression in the cat.
The final alternative is, of course, to give the cat away to a household with no young children in it. Cats are part of the cat family -- which includes tigers and cheetahs and panthers and lions. Even if they love you and have never lived outside, and have always thought of themselves as people, a cat can revert quite suddenly if frightened or threatened. Hitting a cat, or even shoving or yelling, can be a trigger to an instinctive counter-reaction. I sometimes land a light hand on a butt, or a very, very light tap on a nose to get the attention of an angry cat, but I have learned never to hit. The trauma that causes a cat, coming as it does from the care-giver, mother, loving image, can be irreparable in a cat/human relationship. It can also be a lifelong issue between human parents and their children, when you think about it.