Personally, I would bring 2. One big and one small. I too, prefer to carry a big bag but I can't imagine carrying a big bag around an amusement park all day. If you feel like you need to have a bag for stuff I'd find something small and crossbody. When our family went to an amusement park this summer, I just wore cargo shorts and fit all I needed in the pockets, I didn't need much more than a few credit cards, phone, sunblock wipes & lipgloss. I really didn't want to carry a purse all day and worry about where to put it while we rode rides or where to set it while we stopped to eat. I'd use my regular, big bag for any excursions that you take where it isn't an all day thing.
Have fun on your vacation!