Absolutely go!! Since you're driving I'd stuff the car to the gills with all manner of things from home- coffee machine if you have one just in case there isn't one there & you'd otherwise buy coffee out.
Bring your breakfast stuff & herbs / spices etc that you use.
And I'd make picnic lunches with really good treats (multipacks of stuff from the supermarket etc)
Make dinners v easy & low effort - bolognaise with pasta & garlic bread & make enough for 2 nights so you can have breakfast at the cottage, head out for the day with picnic & snacks & come home to an easy quick dinner.
You can totally make this a low cost adventure & your kids are young enough to not have a clue they're on a low budget holiday- everything's fun at thar age!
Give then a simple project- get cheap poundshop scrapbooks & a pot of glue & bring crayons & pencils & get them to make a memory of each day you're there - do they gather things from nature when you go on a forest walk, shells if you are at a beach, ticket from the zoo, cheap postcards or flyers from the things you see & do & they add their drawings etc.
It gives them a focus on each outing - who can find a really good item for the memory book, gets them looking at things differently - if you find a feather on the ground you can google what bird etc & then it occupies them back at the cottage when you're sorting dinner.
They make great memories when they're older - remember the day we went gruffalo hunting in the woods & you found the hawk feather or the sparrows empty eggshell etc (or whatever) you all get to be big kids for the week!!
I hope you have a fantastic week!