Our DS also has multiple allergies (he is dairy-free, gluten-free, egg-free, and nut-free), so I am with you--I carry a cooler of food/drinks in my car ALL the time and my purse is stuffed with GF CF EF NF pretzels/crackers/cookies.
For us, like you, staying in a hotel requires at minimum a fridge and microwave. We've never stayed at DLR before, but I know at WDW if you call reservations and state the nature of the medical necessity (diabetes, food allergies, etc) they will make sure there is a fridge in the room (If I remember right, they may even forgive the nightly charge for it if it's a medical necessity as opposed to just a convenience item). I'm not sure about GCH and the microwaves--if they have them available I think it would be treated the same way.
Of course as for the coffee pot, I think people bring those for themselves all the time with no problems. The one thing that I would ask ahead about is anything like a toaster, toaster oven, hot plate, etc. Most places forbid those due to fire code, and I think that if housekeeping found one in your room you could even be asked to leave the property

(it's that serious of a fire violation!)
As for the parks, because I carry a soft cooler under the stroller with DS's lunch/snacks, I do carry a letter from DS's allergist stating that he has multiple allergies and needs to bring his own food items--this helps with TSA agents if you're flying, we also needed it at the Olympic Games in Vancouver when crossing into secured areas for ticketed events. (I know that Disney is pretty relaxed about people bringing in snacks, baby food, etc but as DS is getting out of the 'baby' stage and with the amount of stuff we carry in, I feel better knowing I have the letter if we are questioned about it).
Lastly, I would encourage you to consider eating in some DLR table service restaurants. I know that having a child with food allergies makes it EXTREMELY difficult to comtemplate eating out in the 'outside world' (for us, just about every Italian restaurant has been off limits for the past four years since DS's diagnosis--there is literally NOTHING there for him to eat) However, as with all other facets of Disney hospitality, they are head and shoulders above the rest in how their food service approaches special diets.
When we've made table service reservations as WDW, we tell them all of DS's restrictions, when we arrive, the Chef comes to our table and presents our DS with choices (for instance he's eaten Quinoa pasta, hamburger with GFCF rolls, tapioca rolls, chocolate cake). Giving the restaurant the advanced notice of a guest with a special diet ensures that they can have good options available. If the restaurant is a buffet, the Chef walks me through it and we determine what DS would like that is safe. The Chef then goes to the kitchen and they send out a plate from the back (to prevent guests from unwittingly cross-contaminating items with shared utensils, etc). I've found that Disney is good in NOT buttering everything under the sun and letting the guests add butter themselves which really helps increase his options (as opposed to other restaurants that add butter on all veggies, etc).
The first time we went to WDW after DS's food allergies were discovered, I did massive research and was pleasantly surprised to find that Disney trains their food handling staff in allergy diet concerns such as cross-contamination, and at that time (this was three or four years ago) I think they had a chef with Celiac on staff who helped with sourcing allergy-friendly options. I think that Living Without magazine has even written articles about Allergy-Friendly Dining at Disney.
We ate Thanksgiving dinner at WDW one year, and he ate Turkey, Green Beans, Cranberry Sauce, tapioca rolls, and a special fruit dessert--he only had to pass on the stuffing (which he wouldn't have touched anyway) and mashed potatoes. This year we'll be at DLR for Thanksgiving Dinner and are really looking forward to it! (Since we're driving this time, I will be bringing our usual foods plus our own pumpkin pie for him--he discovered pumpkin pie last year and LOVES it

)
We've had such successful dining experiences at Disney, they really take the stress out of DS's allergies, that it makes it hard to vacation anywhere else (as if we'd want to LOL!!)
HTH--and have a magical time!!
