It depends on where you will be but a lobster bake only requires one big pot and it's delicious and fun.

You could bring along a slow cooker and have a part of meal cooked for you there. (Not sure about your space limitations)

What about a simple pasta dish (you can make some pesto and store it in a tupperware to bring with you) or even risotto...one-pot wonders are the best!! Use the pesto as a spread on eggplant...slice them, pop them in the oven and top with pesto and some ricotta or shaved Paremsan cheese as an appetizer!

i'd go with a chilled dessert - something like a stellar pudding or mousse you could make early in the day. if you have access to a bbq - steaks and corn are always winners, and scallops/shrimp to start?

and i love the slow cooker idea...

This doesn't help with menu ideas, but every year I cook a full Thanksgiving dinner in a small cabin in Colorado. There's never an issue of missing items because we ship a box of them out. I've pared down what I really need over the years like I use disposable pans and heavy items like mixers etc are definitely out, but if you're creative you can only send a small box and then you don't' have to worry about car space.

Will there be an oven? If you can bring a small cooler from home, you could make puff pastry ahead of time (or buy it), freeze it, and then blind bake and fill it when you got there. You could make individual sweet or savory tarts, such as goat cheese and zucchini, sauteed mushrooms or macerated berry millefeuille. It ends up looking more impressive than the effort warrants ;)

Otherwise, why not research what will be in season in the area and put your effort into selecting the best, freshest items in a simple showcase? As Atthefarmersmarket said, lobster in New England; or have artichokes and/or avocados in California, etc. Local cheesemakers may have some fantastic regional specialties that you can't get anywhere else.

Be flexible. If you can't do gazpacho because there's no blender, try panzanella instead (basically all you need is a bowl and a knife).

Try some twists on simple classics. This summer, I had a fantastic riff on a caprese salad in which firm peaches were substituted for tomatoes, and mint for the basil.

first: a composed salad; avocado, melon, shrimp? cold and out of your way or maybe Vietnamese spring rolls? again cold and done a little ahead
main: most rentals have a grill; if so, steaks or kebobs or pork tenderloin. if not, roast a couple of chickens. rice and grilled or roasted zucchini and tomatoes
dessert: peach pr plum cobbler or crisp

Crostini are a great appetizer and require little equipment other than an oven or grill to toast up the bread. I particularly love the combination of fresh ricotta, honey, and cracked black pepper, as well as pesto, avocado, and arugula. You could serve them alongside a fresh tomato salad, just drizzled with some extra virgin olive oil, good balsamic, and some fresh herbs.

Depending on when you're planning to do this, you can make some yummy and impressive comfort food like a big brisket or pork shoulder, which braises for a while in just one pot. Otherwise, I like the risotto idea which doesn't require any special equipment and is just so good.

A fruit galette is a really impressive looking but easy to put together dessert. With the exception of a rolling pin and some sort of pan (a cookie sheet, jelly roll, even a large roasting pan) you don't really need anything out of the ordinary, since it is free form.

I also do a fair amount of cooking out of my own kitchen, and when on vacation I like to bring a dessert I make at home before we leave--- cookies and brownies transport well and last in the fridge for a long time. Just pop them in the oven for a few minutes to refresh. Grilling is always perfect because you can grill just about anything after a quick marinade- I usually go with some olive oil, salt and pepper, and a spritz of lemon or orange. While you're at it, grill some extra lemons to squeeze on after, they're fantastic. Pasta's always an easy one-pot meal because you can throw in whatever veggies you find nearby along with sausage, shrimp, scallops, whatever.

A giant salad from a farm stand with a homemade vinaigrette, grilled meats (steaks are "fancy", but it could be anything), berries/fruit in season splashed with a good brandy?? with a plop of whipped cream.

You can delegate a ton of the work too: a couple people chop the vegetation, the *manly-men* tend the grill, one poor sap whips with a whisk the cream.

You'll need a couple knives, a jar to shake and serve the dressing, long tongs for the grill, a big bowl and large whisk for the cream.

Not fancy, but simple and really it's about being with your family and feeling happy and full.

I would probably serve something festive and fun for a meal like this, rather than too composed/elegant. It is family, after all! I'd serve a Lowcountry boil (throw in some crabs or lobsters if you can find them), a big green salad, and french bread, with strawberry shortcakes for dessert. Your only equipment would be one huge pot on the stovetop, and one pan of shortcakes in the oven. You could also get away with using multiple smaller pots if the cottage doesn't have a huge one, boiling each ingredient separately. And if there's not an electric mixer to whip the cream, you can be the judge of whether to labor with a whisk by hand or (yikes!) opt for cool whip :)

I'd go with ingredients that require no cooking for the appetizer and dessert. You can devote your full attention and kitchen space to the main course, and have a helper assemble them for you. ;)

Appetizer: Grapes, crackers, good crusty bread, cheese, olives, salami, and the like, is always delicious and well-received, preferably paired with bottles of cheap but decent wine.

Main: Another vote for easy but impressive one pot meals like pot roast, brisket, or pork shoulder, cooked together with vegetables like potatoes onions and carrots, and buy some fresh dinner rolls and spreadable butter, done.

Dessert: Strawberries are in season!!! Slices of pound cake topped with sliced strawberries and whipped cream! A bottle of strawberry syrup and a bottle of Hershey's chocolate syrup available on the side. Easy, cheap, pretty to look at, and delicious!

I second @Irry regarding no cook appetizers/starter (anchovies in olive oil, charcuterie platter, pickles, or bresaola/prosciutto topped with arugula, parmesan shavings and drizzled with lemon juice and olive oil). Assuming there's an oven, you could do a big roast (pork belly or shoulder of lamb would be good) with a tray of roasted vegetables. Follow with a cheese platter. After such heavy courses, how about peaches in wine for dessert - they can even be made ahead of time. Keep it simple, and enjoy the time with your family.

Icebox cakes and rice krispie treats for dessert!

When my son got married in a rustic cabin in Julian California, I was responsible for making the rehearsal dinner for 32. I made delicious homemade lasagna ahead of time and froze it. I baked a variety of homemade cookies and biscotti ahead as well. Once there, I made a lovely antipasti plate of olives, cheeses, and meats served with crusty bread and crackers, a beautiful salad with homemade vinaigrette, the heated prepared lasagna, and cookies, tea and coffee for dessert. Easy and what a hit. On a special note...this if also good for all sorts of appetites...vegetarians, even gluten free...

I stayed in SF recently in a tiny kitchenette and did tons of cooking- I did bring a really good knife, but that was it. If you get some foil, you can cook both your protein and your veggies in the oven together which is super easy. And as long as you have a large pot, you can make a simple white wine sauce (set aside), then pasta (set aside), then steam some mussels or clams- all done using the same pot for a really lovely entree. Make a nice Caesar salad and toast up a baguette in the oven and you're set.