If we arrive in the morning, and check in isn’t until 3 anyway, can we take DME to a park or another resort for dining? Do we have to take it to our own resort?
Nope - limited to your resort only for DME. You could then of course check your carry-ons with the bellhops and take the internal bus system wherever you want to go. Slower than DME direct, but it should get you there plus shedding carry-ons near “home” is likely a good thing…
Once you’re on the coach you could get off at another resort where it stops first. But you’d have no control over the route so you couldn’t plan ahead! Probably not much use to you if you had an ADR… 