"In order to get along with a Basenji, you have to be at least half as smart as the dog!"
Does he still bark if you put him in another room? If he is feeling threatened by the guest he may need more distance between him and the guests. Don't try to force an approach of any kind. Let him keep his distance.
You might want to teach him to bark on command, if he doesn't already know this. Sounds counter intuitive, but if you can turn it on, you can often turn it off. You could ask him to "speak" when guests arrive, then "quiet", and he gets a treat. The barking then becomes your idea and with practice he may learn to wait until you ask for it. Then fade asking for it. Just a thought.
The trick is to make them understand that cooperation gets things over with much faster than resistance. Once the penny drops they may still not like the procedure but they learn to accept it. Timing is important. If you have had problems in the past, maybe not insisting on too much too soon is the approach to take. As mentioned previously, start small and work toward your goal, but never, ever quit when the dog is resisting or growling at you. If you take her foot and go to clip the nail and she resists, you need to keep the foot, even if you don't clip, until she stops trying to take it away from you, and stops growling. When the resistance stops, praise and release, and give her a break before trying again. If your nerves are shot, postpone until later or tomorrow, but make it your idea, not hers!
I agree with Debra that any health issues can precipitate bullying. But just getting older can make changes to a pecking order. Was she ever the dominant dog? If an animal loses its position that can result in the former underling taking advantage. Another thing to watch for is whether his actions occur when she does something he takes exception to......and it may be something subtle that you are unaware of. Even a look passing between dogs or body language can sometimes trigger a reaction.
Hopefully you will be able to work this out, but once a pattern is established it can be difficult to resolve. And yes, as Debra says, separate them if you can when you aren't around to supervise.
Is there any discernible pattern to his actions? Does he go after her only when you are around, in which case it could be jealously on his part. Personally I would make it clear to him that you won't tolerate his behaviour and that she is under your protection, but whether that will deter him will depend a lot on the relationship you have with him.
I had a similar situation once where my older girl absolutely hated my rescue boy, and she wanted to kill him when he first arrived. I laid down the law and let her know attacking him was not permitted. Interestingly, as he got older the balance of power shifted and I eventually had to intervene to keep him from pushing her around! They never really liked each other and didn't play together, but they did learn to tolerate being together.
She growls when I try to move her after she falls asleep, if she is at the groomer getting nails trimmed, at the vet if they approach her with a needle ...bit generally on a daily basis I don't see her growling. But Sunday I took her on a walk for hunger and there were so me other dogs there. She got along with all but one. An adorable black lab puppy she growled at.
I would say many (most?) Basenjis take exception to being moved when they are comfy, and many "wake up badly" to the point where it is a question on BRAT's list. Basenjis, like any other dog, may be difficult about nail trimming if they haven't had their feet routinely handled. And dog aggression is also common in the breed, so I don't see anything unusual here. How you respond to it will be key to whether it remains a problem. Once a Basenji perceives that it can back you off by growling, it will take advantage of the situation. If you aren't confident in your ability to respond it would be best to avoid situations that trigger the growling, but when it does occur I find continuing whatever you were planning to do in a very matter of fact manner is generally the best course to take.
My first girl used to snarl fiercely when picked up. I just laughed and walked off with her under my arm, and the "sound effects" eventually went away. There is always the possibility of escalation to a bite, but that is far more likely if they have succeeded in avoiding something they find unpleasant by growling.
Training is great, but it helps to recognize when your dog is "over threshold", as in this state they are not thinking, just reacting. You need to anticipate situations and be alert to the signs to work with your dog effectively. Training has to take place when he is receptive to it, not when he is frantic and tuning you out. Appropriate distance from whatever is triggering him is crucial for learning to take place.
It's called "transferred aggression", and is common if a dog can't get to what it would really like to attack. Teach your children to stay out of range when you approach another dog!! Take charge with your leash and don't allow her to get close enough to you or your kids to bite anyone. Yes, you can do some training to try to sort this, but in the meantime just don't allow it to happen. If you can't manage that with a leash, get a muzzle and make her wear it when you walk. If she really nails somebody you may lose her because there are laws against biting dogs. (my boy had dog aggression issues and if the offending animal came close to us I had to be careful of this very thing.....and my two female Basenjis would attack each other if another dog approached when I was walking and barked at them, so I know about the issue first hand)
It is not just Basenjis that can have this problem. Fortunately they are not big dogs! In the longer term, talk to a trainer and/or animal behaviourist. In my case I didn't often encounter situations that triggered this behaviour, but if it's an every day occurrence you should see what is possible to improve your dog's attitude.
I would certainly excuse a puppy for taking off with a prohibited item, but by the time the dog is an adult it should have a good understanding of "no". "Keep away" is a game I refuse to play and there are consequences for absconding with "illegal" items. For the dog's own safety I make it clear what is legal to play with and what is not, and I reserve a stern "no" for occasions when it is needed. If this is a frequent problem, let her drag a leash and take immediate action if she grabs something she should not have. I dislike using the "trade" approach because a smart dog (which Basenjis certainly are) will learn that taking something you don't want them to have will lead to a reward. (otherwise known as "chaining" when you are trying to train a behaviour).
The most important thing is to refrain from rewarding the behaviour.....which means don't play her game and don't reinforce with your amusement, which will be apparent to your dog.
Be observant. Learn the signs and react quickly. A week isn't much time to make that transition, but it seems strange that he isn't using the litter if he was trained to it. I don't agree that Basenjis are difficult to house train, but perhaps males are slower to learn than females. My girls were very quick to understand and become reliable.
On a similar note, how often do you take your basenji to the groomer?
Never! If he's shedding go over him with a hound glove or brush. Basenjis do such a good job of grooming themselves that they seldom need much attention other than toenail clipping and the occasional brushing, maybe a bath if they've rolled in something really disgusting. Too many baths can result in dry skin and dandruff issues. Also, I find dandruff can be a time of year thing.
BTW, I do not see a photograph.