
Have you tried closing the door for very short priods ( for example 5 minutes or so) while you are still in the room and taking no notice of any whining she may do?
Obviously if she is really upset then open the door at once. Also like Digger says try covering the crate with a blanket.
If she is ok for these short periods gradually extend the time.
With regard to chewing and housewreckng , have you tried leaving her with a kong? Or tiring her out with a lengthy walk prior to you going out ??