Assertive is not aggressive.
Caesar is a good people trainer, and I've never seen him become aggressive with any dog ever. And I understand the difference between physical and non. He's not aggresive, he's in charge.

Scattering treats when a dog is behaving "aroused" or aggressive, or out of control is only going to train the dog that good things happen when they get into that state.

Someone like Caesar would be the only case I would see as appropriate for a home, since as stated before.. a new home with no small children or pets is NOT safe, because a friend can come over with kids, or a neighbor's pet can be nearby.

Dogs don't "play" so rough that they remove half an ear. That's aggression. When you're worried that she'll grab you accidentally and do damage, that's a aggression issue. It's not the same as a dog that just jumps on and attacks someone(some pet). But it is still aggression. She has a instinct to grab and kill that is stimulated when she grabs something, especially something living.

You have a dog with aggressive issues, and calling it "arousal" or saying it's a play issue will not change the fact. I would call Caesar's place up and see what they tell you. They might be able to point you to a trainer closer to you that is able to deal with "red zone" dogs. You can't intimidate her out of it, and you can't love her out it, you can only deal with the honest truth of her nature, and hopefully deal with it in a safe manner.
Good luck.