If I remember correctly the single strollers cost $6 when we were there last November. I'm not sure about the double strollers but I want to say around $10 or $12.
Here's my simple resonse to your simple question: I think you should do both.
Now for the long-winded explanation: Bring your own stroller to use for going thru the airport and checking into the resort. It'll be worth it alone to not have to chase the 17 month old while waiting for your luggage, checking in etc. Plus, when he/she isn't in the stroller it's a great place to hold your carry-on, or any other small bags you'd otherwise be carrying. Consider also that you may be going to places other than the parks where there aren't any
stroller rentals - the Boardwalk, pool area or miniature golfing, to name a few.
Now for the renting part. When bus transportation is your only option, and you don't plan on being in the park until late at night, then I'd go ahead and leave your stroller in the room and rent one at the park. You won't have to worry about folding it up to get on the bus, while juggling the bag, backpack, water bottle etc. etc. and then doing it all again on the return trip. Also, if you go to more than 1 park in the same day you only have to pay once (just save your receipt to show at the next park's stroller rental podium).
All the parks have the cool jogging strollers with pockets/netting in the back. My kids loved them and they were very easy to maneuver. The only problem we had was overloading the handles with bags so that the stroller became back heavy. We quickly learned to hold on whenever one of our kids got out. Keep in mind also, that they don't recline, which is why if you plan on being in the parks late into the night I'd go with your own stroller. It'd be much more comfortable for sleeping.
If you're lucky enough to go to a park by boat then I'd use your own stroller. It's a piece of cake to just wheel the carriage on - no folding, juggling, weight lifting involved.
Having said all that, you may find you're using your own stroller for the 17 month old and renting one for the 6 year old. After listening to my 6 year old daughter whine for a half a day we started using our stroller for our 2 year old and renting one his sister. She didn't need to ride in it all the time, but it is quite a distance from one end of the park to another, so those little legs do get tired.
Hope this helps.
inkbounc
