I have to say I haven't heard great things about renting or using other's car seats. I've also heard that many times the towncar services forget to bring the car seat, causing delays in getting to your resort.
I know it's a hassle, but I would advise taking your own car seat. Your child will be more comfortable in his own seat and you can be assured that it's installed properly, since you are familiar with it. Plus, you have the added bonus of knowing it's clean!