Hi Kathy,
You are more than welcome to bring food & drinks inside the parks. There are a couple of exceptions - no glass containers (except baby food jars) & no alcoholic beverages. There is a link on the Disney website that lists items that may not be brought into the parks - click
here.
You are also welcome to bring a cooler for your food & drinks as long as it is not larger than 24" long x 15" wide x 18" high. If you'd like to store your cooler, there are lockers available for rent at all of the theme parks, water parks & Downtown Disney.
If you are visiting Disney's Animal Kingdom park, you will not be permitted to bring in balloons, straws and drink lids as they are a safety hazard to the animals.
You will have to open all of your bags (purses, diaper bags, coolers, camera bags, etc.) when you go through security at the theme parks. Be sure you go ahead and have everything unzipped, opened and ready for inspection. That will speed up the process and get you into the park faster.
Wishing you many magical memories :-) Allison