Yes!!! My guy & I tent camped at Periwinkle Park on our honeymoon roadtrip a few years ago. We enjoyed it, especially just getting up & taking the walk to the beach. The tent area was treed & spacious, & we pitched our tent close to our vehicle. Tent camping there was very affordable.
We loved checking out the islands while having home base right there at Periwinkle. I had been to Sanibel & the Captivas many times before, mostly by boat. The beaches at the north end of Sanibel are perfection. Ding Darling State Park is fantastic - we did the tour, and I'd recommend the kayaking as well. The Sanibel Goodwill store was a neat little stop, and started a fun tradition for us of thrifting for souvenirs. I could go on forever about the charms of this little corner of the world. I'm curious what your experience of Periwinkle was, in a TM no less.
I'd love to make it down there someday with camper in tow!