I just secured a reservation with Greenberg Rent a Camper and they allow pets at no additional charge. It doesn't seem to me that they do golf carts but I didn't ask. You might just need to use a different company for each rental.
There are also third party companies that will rent them, but arrangements have to be made to pick up / drop off the carts. If it's only for 2 or 3 days, it's not really worth the hassle, but if it's for a week or so, definitely worth the effort.