What breed is Lily? Given your avatar photo, I am assuming she is labrador??? Correct me if I am wrong.
Also how old is Lily? You said 'puppy' so Im assuming b/t 6-12 mos of age. (most schools wont accept pups less than 6 mos for formal obedience.)
If shes having dominance issues, then you need to step up to the plate and make yourself the dominant one. You and your hubby are the pack leaders. You need to be consistent with pup and there needs to be consistency between the two pack leaders, you and hubby.
I would suggest starting off by grounding her from toys and playtime for a week. She'll figure out why shes not getting playtime, she's too aggressive.
Also if the biting is leaving marks then that needs to be dealt with otherwise your setting yourself up for an all-out between the two dogs if things continue to escalate.
After grounding her for a week, start off again with one-on-one playtime between you and puppy with just one or two toys. If she shows aggression towards you, grab her by the muzzle and command "NO!" If she continues to be aggressive with you, "pounce" on her, roll her on to her back and let out a deep growl. With you being bigger than her this sends the message that your the boss. Then put her in her kennel by herself with no toys and have her stay for the remainder of the day/evening/night. She'll know she did wrong. Once she's no longer aggressive with you, bring in your other dog for some playtime. If shes aggressive with the other dog, seperate them, "pounce" on her again and let out a mean growl. She'll learn from this that aggressiveness towards other pack members will not be tolerated. Send her back to her kennel, no toys, for the reamainder of the day/evening/night. Again, she'll learn.
If shes no longer displaying aggressiveness towards you or other pack members you may try to work on obedience without distractions.
Command "sit" pull up on her leash, down on her bottom. When you have a hold of that collar you have control of the head. If she attempts to bite, pin her down, grab her muzzle, and command "NO!" (Dont body slam or put all of your weight on the dog, just enough to hold her down). Once you get this aggressiveness out of her system you may safely re-enroll her in obedience classes, until then I would suggest pulling her from the class as a safety precaution for you, other people and other animals, as well as Lily, a bigger more dominant dog can and will tear into her.
Also work on handling her. Try a daily grooming, this is soothing and they learn to like being handled. Then once they are comfortable with that, start messing with the feet, ears, and tail.
If things escalate to the point of drawing blood, its time to turn it up a notch. A dog has three handles, two ears and a tail. Give an earpinch, but remember to always reach around behind the head to the opposite ear in case the dog decides to take a bite out of you. Put your thumbnail behind the ear and put your pointing and index finger over your thumbnail on the opposite side of the ear, and pinch just enough to get her to back off, and command "NO!" while doing so.
If she does attempt to take a bite out of you during this process, its best to get with a professional trainer in your area that deals with aggressiveness. They may recommend keeping a muzzler on her when she is out of her kennel to ensure that she wont do damage. If the trainer makes the assessment that she cannot be controlled due to the aggressive nature, you may have to put her down as aggressive dogs dont normally get adopted out too well. But only consider this after all other means have been exhausted.
Good luck,
Dixie