
I have a tibetan terrier too - hes ok left with the others but left on his own he isn't happy, and this is fairly typical of the breed.
Does she follow you around the house when you are home, like a shadow?
One of the key things to improving my boys behaviour was to stop rewarding him for doing that, so we now make a point of inviting him - and then he gets rewarded if hes with us (ie, acknowledged, fussed etc) and if NOT invited, utterly ignored.
As well as doing that in a general sense, we also did a few sessions of what I like to call 'taking the mick' - getting up and going from room to room, moving on JUST as the dog settles each time, never actually acknowledging they are there so that following you around becomes a TOTAL faff and very irritating.
Once that occurs, then introduce a reason to choose NOT to follow - this is hard for me in a multidog household, if this is your only dog it is much easier. Give her something she can't cart about with her - ideally, a huge raw meaty bone, go for one considerably bigger than her own head, so that dragging it around after you is not a viable option.
Then repeat the 'taking the mick' process, only this time she should rapidly choose NOT to follow you.
This is the key point really, when they CHOOSE to stay away from you and occupy themselves, you can build on that and work your way up to going out of the house, starting the car engine, etc etc.
Through doing stuff like this, I can now go out, or into my garden and leave our Tibby shut behind a baby gate, and he is still there lying quietly when I return. Previous to this he was a shrieking idiotic mess, chewing the baby gate bars and soaking himself in a pool of his own dribble, such was his hysteria at not being able to follow me.