How to remove/prevent standing water at campsite???

This talk of French drains, pumps and hoses for standing water that occurs a few days a year is massive overkill. You can fix the problem with a wheelbarrow and a shovel if you have to. Add some fill. You can use fine gravel, some sand and some loamy soil. Topsoil has a lot of organic matter in it. It will be sticky and will not drain that well. Use topsoil only the top.