To answer your question "Is it common to have both tests (genetic and sweat) come back positive" -- I'd have to say yes "mostly" In text book cases yes, you would always expect them both to come back positive. There are also many cases out there that people have a hard time getting diagnosed because they have one or two rare mutations or they happen to have pretty good functioning chloride channels so their sweat test numbers are normal or near normal -- sounds like in the case of the kids you are talking about neither of those things are a issue so you really don't need to worry about it -- I find it interesting that a doctor would test genetically and then sweat test -- it's usually the other way around, but again not important in this case if you already know for sure the genetic test results were positive -- that means they did find two CF genes in each of the kids. That along with symptoms is enough for a diagnosis -- a positive sweat test is even more evidence added to the pile.
Why would they test the parents? In my experience, unless a parent is having symptoms they are not usually tested -- it is of little benefit to spend the money to find out what the kids genetic tests have already proved.... they got one gene from each carrier parent. Most parents do not need to know who has what gene, unless like I said before, a parent has some symptoms and they think that they may find two genes in one parent (and the other would be carrier only) Even then usually only the parent with the symptoms would need to be tested.
Like Melissa said you can expect some daily treatments and Chest Physical Therapy (CPT) to help move mucus out of the lungs. Mom is going to be very busy with two little ones that age with CF that's for sure! If you live close by I'd say she would need help with just about anything you can manage

Just trying to keep up with two that age without CF can be a challenge

I would also suggest she get acquainted with this website -- everyone here can help out quite a bit with a lot of experience and advice. I think there is also a yahoo group for parents with young kids with CF.
The good news is, with the correct diagnosis now it should help to keep the kids as healthy as possible because they can do some preventative things to help as well as treat their lung infections correctly as quickly with the medication that doctors know works best for those with CF.