Obsessive barking

[coalchaser]

My pup Lily is just over 4 months now, and she's actually pretty great about listening to me for the most part, but not when it comes to barking. When I first got her, she used to bark at meal time when I went to get her food, which took a couple weeks but I broke that habit. However, there are still quite a few things that trigger her to bark (and it's a ear-shattering high pitched bark), and I am having difficulty getting to stop.

 

First, when someone leaves the house (mostly me, but occasionally other people as well), she barks at the door. I have been going to the door and getting between her and the door, and then snapping my fingers at her, which makes her leave the area. But unless I physically go over to where she is, she will not stop barking. However, when she needs to go out, she goes to the door and gives a short bark or two, which is useful so I do not want to eliminate barking at the door entirely, just barking at someone who has left. Can she discriminate between these two reasons? How can I successfully stop her obsessive barking without accidentally discouraging the barking to go out?

 

Second, my best friend (whom I am living with for my last school year) has a cat. Lily and the cat have had very little interaction, because the cat is scared of barking, and of course all Lily does is bark at her. I am not too concerned with them becoming best buds, since this is only temporary, and they both have their own separate areas of our apartment. However, the cat likes to sit on the living room table, and when Lily realizes she is up there, she will go over and start barking. She ignores me telling her to stop, and when I go over to where she is, she will run to the other side of the table out of my reach and keep barking (and will continue moving so that I can't get close).

 

There are other times she barks, but right now these are the two biggest issues I want to handle. Thanks in advance for input!

[coalchaser]

Just as an update, according to my friend, when I leave the house, Lily will not stop barking no matter how hard they try to distract her. And apparently she acts unruly as well (I can't say from my own experience, since obviously this only happens when I'm not there). When I'm leaving for class (or going anywhere and no one else is at the apartment), I put Lily in her crate, and she is silent while I'm gone. But if I just want to run to the store and my friend is home, I would rather leave her out. But with the barking issue, maybe I should be crating her even for these short periods?