I pet sat a jack russell for about 6 years and I was very allergic to him (but I loved him so much, I still took care of him constantly and he stayed at my house and slept in my bed). Trust me, a thorough cleaning after he went home to his owner, was the only way to get rid of the allergens and the hair (boy do JRs shed!).
I am not allergic to my basenji, Ruby and was not allergic to my brother's basenji, Zeke, that was in the house when I was growing up. I'm also allergic to my friends' golden and to their german shephard. That said, I know of people that are allergic to basenjis.
Best to do what Tanza suggests and have your Mom visit with the basenjis and more than once. :D.