We love Sanibel but haven't taken the dogs. You can also try dogfriendly.com. I didn't check to see if they had listings for Sanibel but I've used them before to find places in St. Augustine. Have fun!
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"If you have men who will exclude any of God’s creatures from the shelter of compassion and pity, you will have men who will deal likewise with their fellow men." — St. Francis of Assisi, 1181-1226