I think the whining problem can be handled very similarly as the barking problem...... "trying" to ignore, praising/treating when NOT whining, practicing short leaves for the separation anxiety, etc.
BUT, while I am tough on barking, it's harder for me to be tough on whining. It sounds so much more pitiful. Plus, if I have my choice, I'll take whining over barking ANY day of the week. So, I'm sure that I probably reinforce the whining a bit because I will respond much kinder to a whine. But at least it's not that ear-splitting, glass-shattering barking!!
