How big/small are the trees you're attaching to?
I've literally been 'bounced' in my hammock during a wind gust. The head-end was tied to a small, but leafy tree. The tree was prone to swaying in the wind which was nice in a light breeze, but frightening in a strong wind.
As for the tarp flapping, is the XL cat cut? I don't think it is, but I could easily be wrong. Tarps with a straight edge are difficult to get, and keep, pitched tight along the edges. A little flap is pretty normal. If they are cat cut, then you might try using tensioners on your ground tie-outs to keep the tarp nice and tight overnight.