I definitely would not take a cash advance on any credit card. Most credit cards will start charging you high interest from the 1st day you take the money. For a family trying to stay within a budget a cash advance would really hurt you in the long run.
Since you have until September I would try putting a little bit away each week for your "cruise kitty" spending money . Also don't forget to allow for your gratuities onboard, and tipping taxi drivers and baggage handlers. Your onboard gratuities, drinks, photos, shore excursions, gift shop purchases, all can be charged to your onboard account. Then pay it off within thirty days to avoid interest with your "cruise kitty". How much you spend on shore excursions will depend on what type of activities your family likes to do. A simple snorkel excursion averages around $50. You can look at different excursions to get an idea of activities and prices here