As mentioned, consulting with a behaviorist is a good idea. Before allowing anyone to work with your dogs, watch them work with other dogs to see if their style is a good fit for your family.
I would also make sure all are checked thoroughly by a vet, bloodwork (including thyroid testing) included, to make sure that health issues aren't making one or both uncomfortable. I know of times when a basenji sensed a terminal condition before it even showed in bloodwork. Is everyone spayed or neutered? If not, going into season may be affecting anyone's behavior.
Set up a safe spot for her that can be just for her. If she likes a crate, that can be acceptable. She might prefer a pen with a dog bed or something similar. This may require two layers of fencing to make sure that she doesn't start a fight through the fence. Go back to basics with training - nothing for free. Leave a leash on her in the house. If she growls while on the furniture with you, escort her calmly to her safe spot - "if you want to growl, you can do it here..." Her safe spot is not a punishment, it's just a designated area where she doesn't have to worry about sharing the space with any other canines.
I've had over 200 basenji fosters and have kept newbies behind a layer or two of fencing while they learn how to behave here. Particularly when the more challenging ones arrive, nothing is for free, including access to human furniture. They get 'their spot' in the house (in their pen where they can still see the others) where they can feel safe and not worry about others bothering them. I build up communication and confidence by starting (or going back to) basic commands with every meal (with food sitting at their feet): sit, stay, leave it (a VERY important command), look at me, eat. When possible, we go for walks together, one human holding the newbie, keeping him or her separate, yet close enough to be aware of the others. The outside world can be a good distraction to keep them from focusing on hating the other. When I introduce (or reintroduce) them to other dogs in a securely fenced yard, I start at times that aren't so exciting - quiet times, nap times, etc., not around feeding time or when we have visitors. It is important to not make a big deal about anything. Have the right thought in your head, but be prepared for a less than perfect response. Expect small improvements each time, but make sure she is set up to improve. Go very slow. Don't rush it. That is when failures happen.
I hope you get her under control quickly.