Given that outline I'd probably just eat at the house. The little one would probably enjoy some play/pool time and the rest of you are probably a bit tired from the travel, etc. When you go shopping either pick up something prepared or something you can pop in the oven/microwave and eat quickly. With a big full day at MK planned, the R&R "at home" could pay big dividends.
If you stopped at a Whole Foods there are lots of fantastic and healthy choices. If Sam's Club is your choice, there are items there as well ($8 pizza, chicken and other items).
We arrived for an on site stay last summer at about the same time. We spent time at the pool (Mom slept while I took the little one out) then went out for a fancy Disney dinner. However, Disney handled our bags, drove us to our resort and room and took us to dinner. We didn't do any errands or shopping. Our afternoon was all leisure. If we had to do some work we would have probably just eaten a quick meal at the resort.