"In order to get along with a Basenji, you have to be at least half as smart as the dog!"
Lastly, she has never been “odorless”. Wondering if anyone else experiences this. I see comments of others saying their babies are not stinky... lol.
When you say she is stinky, do you mean her fur or body? Or feet? Or could it be odour from her anal glands, which really is stinky! I've never had a Basenji that smelled if you sniffed the fur or skin, but sometimes the feet (possible yeast) and for sure if they are having anal gland leakage.
With autistic children you might want to look at getting an adult so you can see how they are going to relate to the kids. In my experience bitches are often very tolerant with young children, but I am not sure how that will apply to older kids who have autism.
My first thought was "stop shampooing your dog!" Basenjis don't normally need baths very often (or at all, if they haven't rolled in anything nasty!) You might review what you are feeding her and any other environmental things that could be affecting her.
I've had dog aggressive Basenjis and it's a hard habit to break. Since you say she will settle down and accept a new dog after the initial aggression, that's a good sign. Perhaps more experience meeting new dogs in a controlled setting would help. With my last boy, there was nothing for it but to avoid "close encounters" by changing direction or having him sit at a distance as they passed, but he had had some bad experiences and definitely wanted to get his licks in first! Some Basenjis just don't like other dogs, or sometimes just same sex, and it's hard to get them to change their minds.
From your other post it looks like giving treats to divert the behaviour isn't an option, but asking for an incompatible behaviour, like sitting, might be.....