It's not about being selective - she is clearly telling you she is stressed when you leave. Stress can be exhibited in many ways: soiling, chewing, scratching walls, digging at floors, yowling, barking and general destruction.
This means that you have probably over bonded with her and now she is like the little girl on the first day of kindergarten clinging to her mothers legs. I would highly recommend you keep crating her until this is solved. The risk of her eating something of value or that could hurt her is just not worth it.
You need to create more separation with her in general. She needs to learn to feel safe in the world without her security blanket (you). When you go from room to room in the house you should stop her from following you everywhere. When you get up to get a drink have her stay behind and make sure she does it. Don't let her demand too much attention from you. She gets attention when she earns it not because she demands it.
Then you have to practice coming and going so many times that she thinks nothing of you coming and going. You need to desensitize her to the triggers of you coming and going like: keys sounds, picking up your bag, getting your jacket, etc. This is about spending lots of time practicing.
She also needs to learn how to spend longer periods of time in the crate. This is not so that you can leave her in the crate more, but so that if there are times when no one can get to her for a lunch break then she won't panic.
It would also be good to work on her general vocabulary and obedience. The more she knows the more confidence she has in herself and the world.
Love Them & Lead Them,
~Elizabeth & Doug
Dog Training the Way Nature Intended