I can see why someone would think there was Terrier, but I'm not so sure about Basenji. (The only way to know for sure is to do a DNA test.) Both of your dogs look very similar. What breed, or mix, is the older one?
We also have a possible Basenji/Terrier (Yorkie) mix. I've had some doubts, but seeing this picture of Rosie, I can't help but see my Rebel. Such a great looking dog, and if she's anything like our girl, you're in for a treat!
You are in Florida… a sad hotbed of byb/puppymill country. Yep agree with the rest, looks basenji to me too. You might contact Pam Hamilton because she'll know if you are in the hoarder area. I'll ask her to check in here.