My DD has multiple food allergies too (wheat, egg, soy, milk, peanuts, treenuts, shellfish, oats, nuts, most seeds, including sesame). We managed a cross country vacation a few years ago, it went so well that I don't fear long car trips anymore.
So many others have already offered good advice, so I'll just offer a few tips from our experiences: before you leave experiment a bit and find something that you can make on the road. We found a safe canned turkey at Costco, and I started making a simple turkey salad with it. Turns out now to be a staple recipe now. It mixes the drained, canned meat with cut up apples or pears and shredded carrots, and a quickly mixed dressing of lemon juice, oil and salt and pepper. I prepared it at rest stops, I prepared it out of the back of the minivan in a gas station parking lot, and in hotel bathrooms. It's still a favorite. And having a lot of apples or pears handy is great for snacking.
There's a website where you can search for recipes based on the ingredients you have on hand, and I'm sorry I don't have a link to it for you. It may not give you a workable non-cooking recipe, but it could give you ideas.
Bring *everything* you need to make your meals and snacks (or research to see if some of the stores you normally shop at will be available to you on the road, and call them to see if they carry some of the staple foods you need because stores in different areas don't always carry the same brands.) We brought a few pots, too, because we stayed in a hotel with a kitchen.
You'll still need to wash up some things, so bring your brand of soap and a dish scrubber, but cut down on the work for yourself with disposable plates and utensils.
Do your travel companions understand ahead of time what the situation is? Make sure they are clear about what you need of them regarding food. You don't want to find out midway through your trip that they don't "really get it," and it will help them heading into it to make a plan of how to address their needs too. We traveled with my mother, who never really got it and kept trying to bring stuff into the car. That was tough. We spent a lot of time waiting around while she went into places to snack or eat something that we wouldn't allow. And boy, did she ever feel the need to eat constantly on that trip. It was like the monotony of being a passenger made food her obsession. And I learned a lot about how NOT understanding she really is about our situation. Planning ahead for time for your companions to eat other foods in restaurants or rest stops is a good idea so that hard feelings won't develop.
Good luck with your trip!!

I just thought about something I WISH I'd always had along when we travelled & moved when PA son was a toddler:
A DUST BUSTER (mini-hand held vac).
If you have room under seat of car, you could put this in & always have it to do spot vac of hotel before hubby brings child in from car! Places where I find peanuts & food crumbs in hotels are: under edge of bedskirt, under recliner/room chair with skirt, in the fold of recliner, in the sofa upholstery.
NO matter how "clean" the room is, they always miss & sometimes it's due to limitations of the big vacume which cannot get into corners. Plus they rarely do the upholstery, unless you are in VERY pricey hotel (& even then, it's hit or miss).
I ALWAYS am the one to go into hotel room before kids & DH. I check under everything & do cleanliness inspection of entire room/suite. If it's unacceptable, I go straight back to front desk (or call them) and have them get on it ASAP.
BUT -- sometimes it's horribly late & everyone's exhausted (like when moving) and really, all that needs to be done to protect wee one who puts everything into mouth is to have a Dust Buster to spot clean & give some peace of mind.
I know this is not about food, but it just occurred to me & wanted to share, especially since we've done umpteen moves in past 6 years.
Excuse typos, trying not to burn dinner!
------------------
~Eli[b]Z[/b]abeth,
Mother to 2:
DD age 5, NKA, treated as though PA/TNA
DS age 8, PA, possible TNA, Latex, legumes?
(PA diagnosed & ana reaction 1999)
Member here since 2000