If you can, I would maybe suggest you try to take two single strollers instead of the double. It will be much easier to get around and after a long day of walking. The weight from a double stroller will wear on you.
If you decide to stick to taking a double, I would go with the Duoglider FTB. The seats recline, the kids have their own space and it is narrower which will be MUCH easier getting around the park with the crowds and tight corners and such. Although the Chariots are VERY nice strollers and may be more comfy for you to push all day. We have the Zooper Tango SBS and a double jogger SBS. Our jogger is significantly lighter but it doesn't offer the storage or reclining like the stroller. It also doesn't turn like my stroller and it is harder for the kids to get in and out of on their own.
In March my DS's will be 3 1/2 and 1 1/2, and we are taking two single strollers. My Peg Perego single has a toddler running board on the back which comes in VERY handy. So in the mornings if we decide to only take one stroller he can stand on there if he gets to tired or ran over by people when walking. In the afternoons after naps we will be bringing both strollers.
There isn't anywhere you can lock up the strollers. Most people aren't familiar with the Chariot (meaning its a really nice, if not the best jogger!) but that doesn't mean it won't get messed with. I have NEVER had a problem with any stoller we have taken, knock on wood.
Do you think your Duoglider will offer you everything you need during your visit at DL? If so I would say go with that one.