[adpiucf]

No. This is not a good idea. In fact, it is a terrible idea. You are basically using a lawn with no seating and no shade, and this is a horrible impression to make on parents. If you're going to do this, you must rent a table, chairs, and fans.

If you want to have a picnic, try it out as a sisterhood event first and see how it goes. You have limited opportunities to make an impression on the parents of your members.

This event should be paid out of chapter dues, a donation to the sorority, or as a ticketed event. It's great that you want to take on the responsibility of cooking and then donating the leftovers, but you have chosen that responsibility. Attendance and morale will suffer if people are being threatened from the outset that they will be punished. Don't put in the effort if you don't want no shows. People will not show up for a variety of reasons to any event-- even weddings. If your family's offer to do this comes with strings attached, then back out now.

This is a band-aid solution that fails to take into account that people are coming from out of town, that some parents or siblings may have mobility issues that makes hanging out in a park difficult (is the area wheelchair accessible, for example?). You do not have adequate seating, and "bring your own chairs and tables" is a huge turnoff for people traveling from out of town. How will you timely and effectively notify everyone if you have to call it off due to weather? There are too many variables with an outdoor event.

Why not have a reception at your chapter house or at the home of a local member's family? You can host an open house where people come and go over a period of a few hours.

Do not have this picnic. It has disaster written all over it. You need to find a facility or rent a tent for the park.

I applaud you for stepping up with a creative solution in the face of a challenging situation, and your family's wonderful generosity. Keep brainstorming, and the right option will click. Talk to your chapter. Maybe form a committee to brainstorm feasible alternatives. Talk to your advisers. And then vote as a chapter so that whatever you decide, the majority are on board and attendance will be successful.