We have 4 cats (thanks to my DH.ugh) and two rescue German Shepherds.  Our older, male GSD doesn't care about the cats for the most part, but sometimes will chase one if given the opportunity.  Our younger, female GSD that we just got last year will chase the cats every chance she gets.... but so what?  That's what dogs and cats do.  I mean the cats just run and hide and the dog moves on to sleeping, eating, or something else. 

I don't understand why you'd have to get rid of a dog because it chases cats?

The dog needs to be crated every time he harasses the cats. I have never seen a shock collar be effective.

ETA: if it is becoming worse it is probably because now the dog associates the cats with pain (from being shocked).

Did I read that correctly that she's only been in your home for less than two weeks?  That's not much time considering how quickly her whole world has changed.

Was it known whether or not she had prior exposure to cats?

Are you willing to work with her on her exposure and experience with cats?  The little bit you describe doesn't sound as though her behavior with them is predatory.   She can very likely be taught to peacefully coexist with cats if you're willing to make the effort.

What's the story on the shock collar? Though not something I prefer to use, in theory shock collars can have their place in training when used correctly.  It sounds as if she is (or on the way to becoming) desensitized to it which means it is/has not been used correctly.  If that's what she came with it was probably used as a correction every single time for every single interaction and without appropriate release and redirection.  Timing is everything.  If she's sweet natured and wants to please she will likely excel with redirection and positive reinforcement.

If you believe the living situation is not in everybody's best interest (including those cats)  or you don't have the time and/or ability to work with her on it then get her back to the rescue ASAP so she can find her forever home.  The longer she is with you when parting is inevitable the harder it is going to be on everybody.

Just remember there are no quick fixes.  Even if you part with her that doesn't change that she needs to learn how to control her interest/impulse around cats, it just removes the inconvenience from your home.  Dogs want to be good.  Set her up with the best chance of succeeding, even if that's not with you.

Good luck.  

Sorry for the multiple posts, I got stuck on a conference call.  But there are two things I wanted to specifically address from your post: 

You said:

"She barks at the cats, she lunges at the cat, she stares in a very stiff manor. At first she ignored and things were great the first few days but as she is getting more comfortable she sees them through the gate she she lunges and barks at times."  - This is most likely a curiosity combined with insecurity.  From what you describe her body language is not aggression.

Also, chances are this is her real reaction to them.  It's not that she's gotten worse it's that things were so chaotic and new for her that they were not previously on her radar.  She's had time to begin to collect herself and now she's trying to make sense of it.

You said:

"She has a shock collar that she was trained with and we use it we have to hit multiple times to correct her. It is getting worse and not better."   -This is exactly how shock collars are not intended to be used.  Any pressure system is only effective when applied and released at the exact time necessary.  The dog has no idea why she's being shocked or what she needs to do in order for it to stop so she ignores it until she can't.  Your message is not getting through to her.  Please stop using it.

Generally speaking, most training aids easily available to the public are ineffective at best and destructive at worse.  That's because the general public is not properly educated on the aid or how to use it.  And that's okay.  As long as you take the time to learn.  No training aid is meant to be permanent.  Short cuts teach an animal nothing but how to evade their discomfort.  

Please do some research, even contact some local trainers for consultation so you can make an appropriate decision on whether or not this girl is truly the right fit for your family.  This dog is nowhere near a lost cause from what you say, she just needs someone to make the effort.

I just went through a lot of soul searching and advice about adding a second dog to our household. The women at this very established and responsible rescue said that it can take a few months for things to settle down and for everyone to fall into where they will be. In time, they said, all the animals realize the new animal is a permanent fixture and they mellow when they become used to them being around.

I understand your fear for your cats and your other dog, but maybe consider giving it more time for everyone to figure out the pecking order and settle in, especially because your new dog and so good for your first dog.

I wish you luck -- in the end, I decided not to add a second dog, but really because my dog became very sick right after we started the adoption process and I thought I needed to focus on him. I still wonder if I did the right thing by not adopting another now that my dog's irritable bowel "event" is getting better.

Ash, besides the shock collar, are you doing anything else when the dog gets aggressive with the cats? Some dogs can become tolerant of VERY high shock (NOT a fan of those anyway). I have seen dogs learn to tolerate the shock of a wireless fence.

So, are you doing anything else besides the shock collar? Spray bottle of water? Verbal command?