I think Trisha may have a key here. I think this may be less about her being alpha over Carter than it is about reteaching her that YOU are the alpha over everybody. She's forgotten that.
It sounds like Katie's trying to guard against Carter--maybe she's reacting to his deafness as if it were a danger to the pack. Reinforce with her that YOU are the boss in your pack, and if you want Carter there, then he's going to be there. Every time she even looks crosseyed at him, correct her. For the next month or two, force the issue, especially with treats and affection. She doesn't get them except when Carter is present and she's being calm and submissive. If she makes any kind of agressive move whatsoever, immediately isolate her and don't let anyone interact with her for several minutes after she calms.
Max is an only dog, but my sister's two are at my parents' several times a week and since they got a new puppy a couple of weeks ago, Mom's been having a similar struggle with him--he suddenly doesn't want anybody petted in his house but him. She's been correcting him every time, and using a 2 foot lead to tether him to the dining room table, where he can see everything that's going on, but can't be involved until he's let off his lead. She corrects him, tethers him, and then proceeds to pet and snuggle both the other dogs until Max stops barking and throwing a fit and lays down quietly while she pets the other dogs. When he's quiet, she gives him lovies and then lets him loose--until he causes a problem again. Then it's back to the tether.
Max is an extra stubborn Eskie, so the table tether works for him because he's too small to move the table across the deep shag carpet in the dining room, but look for a way to isolate Katie from the flow of things when she's misbehaving that allows her to observe everyone else accepting Carter. This way, it reinforces that YOU decide who gets accepted, not her; and that she gets to be loose and be part of things only when she doesn't pick on other members of YOUR pack.
