I'm not sure about the parks but I would try Walgreens or CVS on Katella/Harbor. It's possible you could find them in some of those stores that are attached to the hotels right across harbor. Is it possible to cut it to for your 4 year old, or is it way too big for that?
Maybe you could ask at City hall once you are in the parks.
If it's a rainy Park day, most of the gift shops pull out stacks of DL ponchos and have them ready to go. We've seen them all over-- Emporium would be a good first bet when entering. They are expensive, but I do recall they have smaller sizes and they are printed with Park designs.
Maybe buy a rain jacket instead? That worked way better for my son yesterday compared to the last time we tried ponchos. We also kept a change of clothes in ziploc bags in case he got soaked and opted for athletic pants over jeans. His shirt stayed completely dry yesterday and we were there for 11 hours in the rain. His pants never bothered him enough to change.
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