I'm sure a nice cosy cottage with you for a week would be fine if, as the others say, the distance isn't too far. I wanted to take our hamster to Scotland with us this year, but it was a long journey and involved an overnight and a ferry so I decided that would be too much stress. As Cypher says it's really important to secure a pet carrier in the car when travelling - don't leave him in his cage as things can fall over onto him, or if you had to brake suddenly he could fly across the cage and be injured.
Don't know if you have a pet carrier but I have the Ferplast Aladino guinea pig size one and it's a really nice size with quite a deep wide base which I fill with substrate and torn up tissue paper and can fit a couple of small houses in it and hide food in the substrate and treats in various places. I've only used it during cage cleaning so far, but sometimes Charlie is having such a nice time in there he doesn't want to come out again! He tends to build a little nest in one of the houses and one of them is a hay covered cardboard house and that keeps him busy for ages ripping the hay and cardboard off the inside to help build his nest!
Anyway one of those would be good for travelling if you don't have a pet carrier. I wouldn't have thought a seatbelt would be enough to hold it in place it would need to be well wedged in so it couldn't move at all, even if you braked - or maybe on someone's knee who can hold it during the journey. Putting something dark over the top like a dark coloured sheet or something might help too, as long as there is still ventilation. A piece of cucumber should do him for the journey instead of water.
As to how long the journey they can manage, I would think this would depend on the age and temperament of the hamster (and whether or not you have air conditioning in your car if it's hot weather!) I think ours would happily sleep in his pet carrier for a good few hours, because he's used to being in it sometimes and would recognise my smell and voice. If he's older or a bit nervy I'd have thought 4 hours max maybe.
Still take his cage with you of course, but don't do what I did on a short journey and forget to empty the food and water bottles, or you end up with a big mess! Also might be an idea to put it in a big black bin bag for the journey (the cage that is, not the hamster/pet carrier!) in case bedding falls out.
I think it sounds like the best option for your little older one. Leaving him at home without disturbance is also a good option but only if you really are happy with the person coming in to care for them. It's really difficult! I couldn't leave Charlie at home or take him with us so took him to someone else's house (another member on here) but he was still very stressed by the change of environment - he had to go somewhere else, then 10 days later come back again probably thinking he'd left forever!
A friend of ours recently told me about a really good pet-sitting service though where they will come to your house and do their food and water and even let them out if you want them too. Maybe there's something like that in your area? Someone highly recommended by others maybe who will do just what you want. But I think you'd be happier having him with you or you'd be worrying about him. If he is bonded with you I think he'd be better with you really - the change of environment is less of an issue as long as the person is the same