While $1300 might be more than enough (and I don't know, it depends on ages, eating habits, and how much you do or don't indulge your kids), make sure you take a credit card.
You never know if you are going to have to take a puking kid to a doctor or emergency room; or need to replace a blown tire; or have any other emergency that could kill your vacation by taking most of your cash. Even just getting a nail in the sidewall of a tire can be a very costly repair. It happened to me right after I bought my car, and we spent over $200 on a new tire (and I don't have a very expensive car - it was a standard SUV tire). That's about 15% of your total cash if you don't have a cc to pay for it.
The cc will make sure that you don't have to scrimp through the second half of your trip or waste a day waiting for someone to send you money via Western Union.
I would never travel w/o at least one cc.