A small challenge when moving is how to keep things cold. I speak from doing this many times. Sometimes the room fridge is more of a drink cooler, and there is no way to freeze cold packs.
Also, some meds and toiletries don't do well when they get too hot.
Cars heat up quickly in FL, esp in summer.
One tip trick I have learned is that soda cans stay pretty cool for quite a while, and they are somewhat easy to find. the hotels bell services will - or used to - be willing to keep some stuff in a fridge, but I would check. It was getting overrun by grocery deliveries. It also takes time: returning to bell services, waiting in line, etc)
Eating at Universal, IME, is a little more reasonably priced that WDW, at least if you want to eat on the cheap. I also feel like...they make it easier than WDW to have what we need. Like, for some reason finding plan rice at WDW is nearly impossible. Universal has Panda Express. and way more variety of beverages.
Love 2.5 gallon bags. I also often pack sandwich bags, a few 1 gal bags. You can buy reusable grocery bags themed to WDW or US (or bring one). Those can also be handy when trying to move between rooms in a hurry.
With small children, I'd likely also try to recruit their help and cooperation. We used to go to WDW with extended family all the time and having them make a thank you drawing/note for housekeeping was a great way to keep them busy every morning and they had fun.