When she is left alone, are you sure she is shivering because of the cold? It sounds like she may be shaking due to her nerves and anxiety.
Dealing with an anxious dog is hard-you have to figure out what is making them uncomfortable (which is tough when they can't explicitly tell you), then figure out how to make them less averse to that thing that made them uncomfortable in the first place.
When she is alone, does she whine and bark? If so, this is her crying for help-and her training you to realize that if she is uncomfortable, you need to do something for her. To get her to stop whining/barking, you have to let her cry herself out, then reward her when she has calmed down by visiting her or giving her a "good girl" from the other room.
If you think your dog is uncomfortable when she is alone because she doesn't know what to do with herself, sometimes dog toys can help-I'm a fan of "cow hooves" as chew toys, as they last a long for my dog and chewing helps her relieve anxiety. Those might be a bit big for your pup, but something that can be chewed on for a while (a rubber kong toy filled with peanut butter, a squeaker toy, etc) may help her alleviate boredom when she is alone.
When you guys are just hanging out at home together-is she usually perched on someones lap? There isn't necessarily anything wrong with letting your dog sit on your lap-but make sure she has to ask permission first (either by giving her owner or the person whose lap she's wants to jump into a look and waiting for an affirmative response). If she assumes that she can jump into anyone's lap she so chooses without asking, this may indicate that she thinks she is in control of the situation. That is not ideal, as dogs who set their own rules are less likely to follow the rules we want them too (like not barking when left alone or when strangers are around).
I had a husky mix once upon a time who started off as a great dog-and then as he became more comfortable with us, he became less and less well behaved in "anxiety-inducing" situations (i.e., meeting new people and dogs, which eventually turned into just seeing strangers or other dogs); he would bark and raise the hair on his back, and it got too be a scary problem, as his anxiety made him harder to control and communicate with. After consulting with a dog trainer, we stopped giving him attention when he asked for it and only gave him attention as a reward for when he obeyed a command we gave him. Upon coming home from work, we would wait to greet him until we had put all of our things away and only once he calmed down would we say "hi." Within a week we were able to let him meet new people and dogs without any negative or anxious reaction.
Moving can be a scary experience for a dog-and it may very well be natural for her to exhibit this type of behavior if this is what she believes is expected of her. However, it's never to late to recondition your dog to act how you would like. She is a very smart and very cute girl and I wish you the best of luck.