I agree with you that "personalities don't clash" actually is a factor in whether 2 of any dog breeds get alone, especially basenjis.
To the OP, I am not sure I agree with the poster saying the older female is showing displeasure at the younger being there. It is entirely possible and NORMAL that she is trying to discipline her. If that is the case. your interfering will escalate the problem. If there are simply horrific noises, if no blood is drawn, you best chance of this working is to allow her to correct the pup, supervise the pup and feel comfortable that the new female is not going to take her place or challenge her. Will it work? See top line. If the new pup stays docile and doesn't challenge her, then you could have a life of fairly peaceful coexistence. If not, you could have to separate them for the rest of their lives. You have to decide NOW if you are willing or able to do that. If not, sadly you have a problem because the saying is right– it works til it doesn't. While many family have 2 of the same sex or even 3 or 4 that live happily together, you can't bet on it. You have to know that any time you add a new pet, you risk having to run separate packs.
I did NOT want a male dog, even though I had a female here. The good part is that at 7, she had never shown any desire to lead the pack or be aggressive to the other dogs (she grew up with 3 rotties, a chow/coyote and another basenji-- all dead at this time). I got Cara young. Cara also, at 2, so far has not shown any dominance issues other than bed guarding and over food. Food i solved easily-- they already have meals in crates-- they want a treat, Cara knows to get off the bed or sit back while I give Arwen's her treat first. Bed, if she snarks I make her get out of the bed and hit the floor until Arwen is in bed and comfortable. But do I seriously delude myself that because SO FAR it is okay that it will stay that way. No. It could change tomorrow-- something set them off, a fight ensues and the likelihood of harmony goes down the toilet.
I think other than interfering in their quarrels you are doing just fine. But we do expect pictures here. Alex should make it a first post requirement