Norm: You don't mention what your wife does for a living. Nor do you mention if you have tried obedience training with Westley, have you? I would suggest that as a possibility, but be prepared for it to take a while because Beagles are notoriously hard-headed. However, if you use treats with the training, it should expedite the work. There are many activities you could do with Westley that will help. Obedience training not only teaches the dog to obey, but also allows him to know what his place in the "pack" is (which of necessity, must be lower than you and your wife). Whichever of you takes him to obedience will find him bonded more closely to that one, so you should plan for both of you to work on the training.
I can't entirely agree with Carrie. The Beagle IS a working dog, but with work can be a great companion dog. If you can work with him on weekends there are many things you could work with him on that would utilize his natural abilities such as agility, tracking, flyball, etc.
Would a cat companion for him be a possibility? Living in an apartment with an active dog is tough -- been there -- but with some work, it can work out. I also liked the suggestion of an older resident "doggie sitting". Have you looked into that?
I feel your pain -- we were evicted from a trailer park unjustly because the neighbor complained about our dogs barking and it was the dogs on the next street over. Oh, well, we survived that -- dogs intact (so to speak) and I had three dogs and a cat at the time. Give the obedience a try and see if that doesn't help. Good Luck.