I don't really know how fair of an assessment you could make after only a day...moving to a new home with new animals, people, and routines is an extremely stressful situation for a dog. Honestly you say you're excited and ready for a dog, but just from this post and some of your other responses to others it seems to me that you aren't being totally honest with yourselves about how prepared you truly are to adopt a dog right now.

Not only are potty issues fairly common when switching to a new home, it's extremely common in smaller dogs in general even when potty trained. Also, separation anxiety can be managed with exercise, proper training, and a routine so the dog is comfortable. You didn't really allow the dog to experience any of that with you, and then you blamed the old owners. They may have lied or embellished the truth, but you honestly have no way of knowing because you didn't even give that dog a chance. Every dog has unique personalities and issues and everyone has to work through certain things with their dogs, so if you just want to get a pet that you don't have to do anything with, maybe just get a fish or something.