at 3 weeks i woudl not worry at all about that - this is the most portable stage IMO. just keep an eye on when he is tired and hungry and ensure he has some A time each cycle. at 3 weeks most of their day is eating and sleeping - a weekend away won't make any difference as your main goals are to ensure he knows day from night (by limiting each of his naps to 2-2 1/2 hrs if possible in order to wake for a feed and brief A time), goes to sleep from awake (rather than nurse/feed to sleep) and you observe him to learn his cues, temperment and such.
enjoy this time with him.
as far as falling asleep in the car - it is normal at any age if they are tired and just sitting in a moving vehicle (car,pram, anything in motion). as long as you don't use a car to put a child to sleep for all naps it is not a worry. if you can time things so that he is not in the car immediately after the feed (allow for some A time - at this age VERY short) and then don't worry if he sleeps in the car. when he is older and more aware then you will want to work on ensuring most of his naps are in his bed.