Barking: Jack Russell female

Question
I have recently started long-term babysitting my sister's Jack Russell puppy (she is about 1 year old), and was told she was quite the barker before I took her in.  I have two cats of my own, and she gets along with one of them really well - the other hates her unfortunately, and avoids the dog as much as possible.
Since the begining, I have tried to establish myself as pack leader, with the cats above her also - seeing as they were already here, by the usual methods (feeding her last, keeping her at ground level unless invited up, etc [Are there any other methods that might work better?]).
She hardly barked at all the first week, but has gradually worked up to constant barking if outside at all.
What can I do to prevent her being too noisy for our elderly neighbours (who have a maltese terrier) when outside?
Also, are there some teaching techniques that work well for her breed?  I am finding that with treats, she focuses on the food, and not why she got it. It is like we start from the begining every day :/
Other Information You May Need to Know:
We take her for walks at night, and I try to play with her throughout the day though usually only about 3 times a week.  
Inside, she is quiet unless the front gate bangs, or a loud truck or motorcycle goes by - this doesn't worry me.
Also, one of my cats is on heat, and toms keep hanging around.  I found two in the back yard this morning.
She is not used to rules.
She is not desexed - yet.
She is very placid and gentle, never bites - even when I cut her toenails! although she wants to.

Answer
Hi Kelly, that's good of you to care for your sisters puppy.
The very first piece of advice I would give your sister is to have the dog neutered ("de-sexed"). It's important and much easier when they are younger (4 months old is the typical time) and can help control some of the aggressive barking she is having toward the Maltese and other dogs.
It's hard to stop barking unless you are physically with the dog when she is barking. You have to immediately correct the behavior the very second she starts. You do that by interrupting her train of thought by breaking the dogs concentration with a sound or touch correction (make a distinct noise, point your finger, touch the neck) the second she opens her mouth to bark. Stay consistent and in control. Barking is such a deep seeded and ingrained canine behavior that you probably won't be able to stop it completely, but you will be able to control it more.
Food is an excellent training tool. Just make sure you don't give her any reward until you get the desired result. I know it can seem like an eternity waiting for them to do what you want, especially when they are sniffing and all excited because you have a treat in your hand. Don't give in until you got the result you wanted.
You can teach her TO bark on command by using a word "Speak" and rewarding her with the treat....and then use another word, "Quiet" reward her when she is NOT barking. Eventually she will learn the difference between the two words!! As with any training it takes LOTS of patience, and lots of focus and time. One good thing is she's a jack russell and they are super smart and learn fast!!  Just stay completely consistent.  
There are also bark collars and other devices on the market that are helpful in curbing barking, but I don't suggest any collars that shock the dog. They make collars that vibrate to remind the dog to stop barking, and you need to spend time training her with the collar and your voice command at the same time. Eventually, hopefully, you can get rid of the collar and she will obey your voice command only.
Barking is the hardest thing to control, and I've given you a lot of examples here. You can pick what works for you. It sounds like you are doing a great job with her, your sister and the dog are lucky to have you!!
Best of luck!
Carol