Why is my dog so aggressive?

We have had our dog for a year. She came from a home that kept her tied up outside for the most part and had to be given away for getting off of her leash and attacking the neighbors dog. We have had her sister from the same litter for 3 years so they're both 3 years old. Both dogs are up to date on shots, heartworm medications and both spayed. Since we have gotten the other dog she's been very kind to the immediate family (i.e. my fiance', brother and dad). Recurring members of the household she shows aggression toward, like my brothers girlfriend and friends. She corners them and goes right for their throat but backs down when one of us scolds her. We just figured it's because she wasn't socialized enough and we could help her. She's gotten worse within the past couple of weeks though, she has started going after other animals in the household. She has snapped at our senior cat multiple times and gone after her sister more times than I can count. It all started on christmas when both dogs received 2 very large bones, she just snapped and went for her sisters throat. She's the sweetest dog and has never shown any aggression toward the family or animals before christmas. I'm just worried we may not be here to stop her in the future. She's a doberman, collie mix breed and I was just wondering if anyone else has ever had this problem, maybe it's a neurological disorder or something worse. I don't think it's behavioral, she's never been physically abused, her first owners loved her very much and come to visit her a lot and she doesn't show them or their young children any aggression. Also note-worthy, she didn't come to us spayed, she was spayed about a month ago and given all of her shots and she has only seemed to get worse since then. She also shows no aggression outside of our house, we take her for walks and to the vet and park and she never shows a hint of aggression, if anyone approaches her she immediately lays down and lets them rub her belly.