Okay, so many things to respond to.
Please define what you mean by "discipline".. because I am sorry, I have Rotties, chow, and do rescue of dogs who need retraining for aggression issues. I don't "discipline" so much as I train. And let me be clear… I sit here with on hell of a hard line of rotties... schutzhund/german lines. I train. Train right and discipline is minimal. Nor does it really work well with chows or basenji.
2nd, if you knew the boxer was aggressive, why the heck would you take your dog and brother's dog NEAR the dog? Would you take your toddler to play with a bully? Your dogs can learn to bully, they can learn to mistrust and attack, etc from this dog. Please do not allow your dogs around this neighbor's animals again. if they do not have the sense to keep their boxer under control, then it is your job to protect your own animals. While playing with GENTLE other animals is sometimes great, they do not ever need to play with such dogs as that, period.
I agree with the others, you need to find someone within spitting distance of the clue bucket about training in a positive way that will work with a basenji.
Also, doing rescue, if a dog is not here long term, I see no need to work that dog completely into my pack. A few weeks isn't long. So you need to totally supervise them and simply remove your senji when she gets rough. She will either learn to play nice, or learn that rough gets her crated. It is actually a VERY good training experience for her.
My husband takes my male rottie to play boomer ball. Keep in mind my youngest senji is 5. We have to crate her every single time because she attacks him when he is playing with my husband. She chews on Connor like he is yak meat. Its not okay, he shouldn't have to put up with it. So her little nasty butt goes in the crate. I can't make her play nice, but I can protect my other dog from her nastiness.
My point is we can't make them perfectly behaved dogs, but we can control the extent of their not niceness!
As for your sibling issues, lol... I am the baby. I don't listen to my siblings, they don't listen to me. Even if your bro was the best trainer on earth, it might be best to get nonsibling help. Its just the nature of families