Hi there, this is Miranda, not Jason this time.
I want to tell you that in our house, Roo has a very different relationship with each of us. Roo is definitely crazy about me, and will Baroo for me (sometimes but not as often as he does for the kids…) and play with me, his favorite thing is to sleep in my lap though. With Jason he never ever Baroos (until last night!) He Baroos as a welcome home to me and the kids but not Jason.
With Jason, Roo is very very motivated to do tricks, not as much with me. The pacing, and whining you describe happens here too, when Jason goes out. If he leaves the house Roo paces and whines, scratches the door, etc, until he hears the car start and realizes that Jason isn't coming back in. He will scratch the door when someone else goes out, but none of the anxious behaviors that he exhibits for Jason.
With time, your girl will establish a unique relationship with each of you. That is one of the wonderful things about Basenjis. They are independent thinkers. I think you may not have enough of a feel for Basenji psychology and signalling yet. It is obvious from your posts that your girl is bonded to you, but she doesn't see you as a playmate, she sees you as the boss. Try teaching her some tricks, or obedience commands. I echo what others have said about finding the yummiest treat possible for her to use during these sessions. Freeze dried chicken, or fish is one thing you might try.
Basenji Bonding from the Male perspective:
Miranda and I wanted to give both the female and male bonding experiences from our experience.
First and foremost, I think your Basenji sees both of you, the male and female in your household as pack leaders. Since Basenji's are highly intelligent they do sense that different pack leaders offer different things and relate to them in different ways. It has taken almost a whole year for me to get a Baroo out of Roo when I came home. Ironically that only happened last night. I cannot comment as far as what his behavior has been when I leave him with Miranda but I know Miranda has already covered that is her response in this post.
Roo will cuddle, sit on my lap, wrestle, bring me toys, and retrieve for me. Of course he spends most of his time with me. The best bonding you can do with your dog is to take him on long walks every day. Now that the weather is starting to break this is a good opportunity for you to do this. We walk 3 miles in the morning and 3 miles in the afternoon. Miranda sometimes meets us at the park in the afternoon after work. She is more regular in doing so in the summer. This activity is good for both you and your dog.
If you also take a longer leash to the park, you can switch leashes and let your dog have some running room after his/her walk. I take a 20 foot lead I bought at a dept store and I found that if you just give your dog about 15mins every day to do this after the regular walk it has an impact.
After you do walk your dog this is a great time to train and teach him/her to sit. I take Cheerio's with me as treats. I give Roo and Bonzo(our Boston) Cheerio's after our walk. They have to sit to get them after our walk. I also train Roo to sit, come, and retrieve with Cheerio's. Since I am going to start agility training after he completely recovers from his Neuter, I will most likely use Cheerio's to reward after that.
I noticed you say your dog is not food motivated. That is ok. Maybe since the dog sees you as the main pack leader he/she is a little more tentative about taking a treat from you than from your wife. Keep in mind that in the wild, dogs usually do not take food from the pack leader. They wait until the pack leader is done and walks away from it. Since this puppy was 6 months old when you got him/her, this puppy might have already been in the habit of treating the pack leader different and respecting the hierarchy of the pack, especially if your puppy was keep with several other dogs.
One last thing I would like to mention. Basenji's as well as other dogs are very very smart when it comes to sensing or reading people. If they sense any kind of fear or stand offish behavior about you, they can reciprocate in kind. I am not suggesting you do what I do. I can honestly tell you that even after owning many dogs in my life, I had no idea what kinds of behavior I could really expect from owning a Basenji. There are lots of stories on the web about different ways they can behave, and some include aggressive behavior. You can buy into those types of stories or find out for yourself. A lot of how your dog behaves is related to how you handle him/her and what you expose them to. In my opinion, how much control you have over your dog is directly related to you and your relationship with that dog.
I did have fear of being bitten by Roo's Razor Sharp Puppy Teeth. I do not know if there is anything I have experienced that are sharper than a Basenji's baby teeth. Since Basenji's like to mouth and it can be their way of letting you know they want to play, I think it can often be misinterpreted. People do jerk their hands away because they are not used to this type of behavior, and as a result they get scratched and think the dog has attempted to bite them.
I got over this very quickly by sticking my whole hand in Roo's mouth. In fact it is a practice I continue today. I also can grab Roo anywhere, including yanking on his tail and ears. Roo never attempts to bite me, but does continue the mouthing behavior when he wants attention. We have accepted this mouthing as normal and spent a lot of time when he was a puppy sticking our hands in his mouth and teaching him not to bite.
Once again what works for me may not work for you. I think if you are patient, you will find that your dog is very bonded to you, and happiest when all his/her pack members are present.