Woe woe woe WOE! You already have one animal with a behaviour problem. This doesn't mean you are "bad" pet owners by any means. What he's doing is perfectly naturel for him. He is displaying a domminant behaviour to your child most likely because he feels he can get away with it. However it is some thing unacceptable that needs correcting before anymore pets are introduced! If more pets are introduced it is likely it will only distract from the problem and chances are you could end up with two scratchy biters on your hands! I think you are right in thinking another cat would be beneficial to him. He would have a fellow feline to play with. I think before you do this you need to set the boundries.
First off it is NOT acceptable for him to be biting your 9 year old. Encourage her that when he does this she makes loud sounds that indicate to him that she is in pain. I have no doubt your children love your cat but think about how your child likes to play with him. Does she tease him? For instance waving her hands around his face and when he tries to bite, withdrawing and giggling at him? This will make your cat think chasing and biting is a game. Kindly explain nice playing with the kitty, (in ways that do not encourage biting scratching).
Buy toys for the kitty to play with and chase (these will be a distraction for him).
Also make a rule of if he scratches/bites then he's not allowed to be petted. Arms need to be folded and the cat needs to be ignored because he is doing some thing bad. Your 9 year old might get a bite from him then feel she has done some thing to upset him and then stroke him. This is a big no no, if he has learnt biting and scratching her gets him attention he's just going to keep doing it!
Look at the reasons he doesn't bite you and your partner and the other children. How do you react to him and how does your 9 year old react to him that is different? How do you react to his scratchy/biteyness in comparison to your 9 year old etc.
Good luck !
Hope I have been of some help ^_^