Hand Sanitizer
Picnics can be messy, especially when your kiddos have been running around playing. Since you may not have a water source available to you, hand sanitizer will come in handy (no pun intended) when everyone needs to wash up before eating.
Speaking of being clean, you may also want to consider bringing baby wipes (they are great for cleaning sticky, messy hands and faces after eating), trash bags and paper towels.
Fresh Lavender Sanitizing Hand Gel, $6, available at Bath & Body Works