We have always used a backpack in the past and that worked good to hold baby stuff as well as other misc things. But the backpack we used was smaller and had a rip so I needed to figure something else out for this trip.
I ended finding a good deal on Skip Hop Saddlebags and bought to for my stroller. They attach on each side and could fold right up with the stroller. They don't look it but are VERY roomy. I had more than enough for all my toddler's things in them (lots of diapers, wipes, spare outfit, sippy, juice boxes, etc) and probably only needed one. We also had some other type of bag to hold our Ergo Carrier, resort mug, Pal Mickey, raincover, etc. but that changed depending on the day and what was needed.
This was helpful because many nights. The 4 of us split into 2 groups. Whoever had the 2 yr old also got the stroller while the other parent took the 8 yr old and the extra bag. Neither of us had to lug around more than what we needed.