DLR has no double strollers.
I've never felt comfy with the idea of a jogger, b/c they are so bulky.
When DS was 1 we rented (he was in it for a grand total of about 30 minutes) a stroller and I wore him in a mei tai the whole day (day trip).
When DS was two we did the same, but I wore him in my Ergo (back carry) and it was MUCH better and easier (and he was on the ground much more).
The above is just to say that with the 8 month old, you'll probably have a better day if you get a really good baby carrier, like a mei tai or an Ergo. My guy was always extremely interested in things around him when out and about, when he was up at shoulder level rather than at bottom level.
For the 3 year old, we've now used the rentals (OK, but when you really need them is for the walk back to the hotel!), a BabyTrend (quite liked that, but he outgrew its max weight FAST), and now a Mac Volo. Like the volo best!
If you have the disney visa card you can get two FREE rentals every day. YOu have to spend the time each morning to wait in the line for them, which takes time away from solid touring time, but hey, free is nice, right? (we do not have a disney visa)
If you don't have the visa and you decide to rent...get the multi-day rental! You only have to wait in the main line once, and the other days you go right to the end, to the person passing out the strollers, hand over your ticket for that day and youv'e got yourself a stroller (or two...I personally wouldn't put an under-1 in the rentals, but others have)!