I cannot believe YTNR wouldn't let you adopt just because you didn't have a house! The only reason I can think of is maybe the barking might irritate other tennants, or maybe you don't have an enclosed area for the dog to pee?
You might be better off starting fresh with a puppy. This way, you can train it to use pee pads from the start, and train it not to bark. I think many of the Yorkies from YTNR are older, and it's harder to get an older dog to adapt to your lifestyle. Maybe that's why they didn't want you to adopt. Well, we all know your heart is in the right place!!