Ping, here are my thoughts, for what it's worth.
Here are the goals:
1) Ping, as the existing kitty, is the priority. Ping's health and happiness are paramount.
2) Tiny needs to be happy and healthy too - but she needs to learn how to behave properly in your home.
To achieve number 2, here are my thoughts:
I agree with GoldenKitty. I think Tiny should be separated in her own room (if that's possible) for a reintroduction. Let her out only for supervised "visits" - and also for "behavior expectations retraining." (A new phrase I just made up
). This will give Ping some "breathing" room.
Cats learn best through positive reinforcement, so forget the squirt bottle. It will only make her scared of you. For the "negative" reaction, get an empty can and put some coins in it. When she goes for Ping, rattle the can loudly - the loud noise should startle her out of the attack if done properly. Say "NO" firmly. Pick her up and put her in the bathroom for a 5 minute time-out. When the time-out is up, do not say a word, do not look at her, just open the door and walk away. She learns that attacking Ping gets her isolated and ignored.
For the positive reinforcement, let her know when she's doing "good." When she is around Ping and playing nicely or not attacking him, or if she walks past him without attacking him, or is laying down near him - praise her to high heaven. Well - praise both of them, because we don't want Ping left out. Give them both 2 treats.
Create as much vertical space as you can. If it's a dominance thing, having the ability to go "up" often helps diffuse the physical aspect of it. Don't know if you live in your own home or rent, but if you don't rent, stuff like this is really cool and pretty easy to do yourselves: http://www.katwallks.com/customerphotos.htm
. Of course cat condos and cat trees are an option. They can also easily be "built" by pyramiding or building "steps up" out of large rubbermaid containers.
But I'd go for separating her first. Go for supervised visits. When she shows aggression, back in her room she goes. I'd do this first for a couple of weeks, though I would use the can of coins to break the attack.
I would definitely at least put her in her own room for the night, so Ping can slowly get back to realizing it is safe to sleep in the bedroom with you.
(His behavior now won't change overnight
I'd also use vanilla on both of them before their supervised visits. Dab it behind their ears, at the base of their tails, on their bums, and under their chins. Find real vanilla - not the synthetic, mostly-alcohol based stuff.
But focus on positive reinforcement when possible. And focus on letting her understand that aggressive behavior gets her ignored.
To that... when she attacks you or hubby, blow a short, sharp puff of air directly in her face. Say NO firmly. It's a little late - but is she teething? Either way, get some bendy straws. After blowing in her face and saying "no," hand her a bendy straw to bite/chew, and walk away. Given that for a few weeks at least, she should be confined for the night, biting you in bed or while sleeping won't be an issue. If you decide not to do this, it's a PIA, but blow, say "no," and give her a straw. If she doesn't focus on the straw but continues to try to play/bite you, blow, say "no," give her a straw, and put her in the bathroom for a 5-minute time out. Again, the idea is to get her to realize that biting a human at all is NOT ok, and it gets her ignored.
...but she is a kitty.
She needs lots of attention and play time (though do make sure Ping always gets attention - play or love, whatever - first). Give Tiny lots of play time in her room - make sure she's not just alone in there all the time. Put up a bird feeder just outside a window in her room or one that uses a suction cup and stick it on the window - and make sure she's got some way to sit at window height. But again - when she's playing nice, not playing with your limbs or biting you - praiser her. Help her understand what is OK and what isn't.