Hi Jay, welcome! Did you have your dog posted on Craig's List? I'm grateful that you found our website, and that you are looking for solutions for Trey. Giving him away before addressing his behavior just pushes his issues onto someone else, who doesn't love him like your family does.
If Trey hasn't been to the doctor, you may be able to find some low-cost vet options. When the economy gets tough and we all pinch pennies. It's easy to overlook checkups for our dogs, especially when the Dr says, "let's run some tests." :eek: That has $$$ all of it, you know? In Tampa, because the vet offices are slow, they are running great specials to keep busy. Maybe you (or your wife) can call around to find someone who will give Trey a good check up without costing an arm and a leg…
I'm glad to hear that your daughter is in 4th grade (versus 4 years old), because she's at an age where she can respect Trey's boundaries. I don't think a basenji would simply chomp on someone without sometime of forwarning... unless he's sleeping, and wakes up grouchy? If that's the case, as long as everyone knows, I don't see her in imminent danger.
Hopefully you or your wife can spend some time reading up on the quirks of a basenji. It's one thing to visit a basenji, and another to live with them. Like Anne said, the basenji breed is very smart and common training methods with other dogs don't necessarily work.
Does Trey get along with your lab? Are they bonding?
It is a lot of change for everyone in the house, including the dog.... mutual respect and love will go a long way. I hope it's a happy home for all, even if times are tough.
I hope we can help you out!:)