S.T.
wow, i thought you were going to talk about medical procedures or tests or sports challenges. if YOU are the situation that makes him nervous and scared to the point of throwing up, i think i'd be looking for ways to ease the situation. this post sounds pretty judgy. their mother moved them 4 hours away, okay, but i'm betting she had a good reason to do it, like she needed a job, or the support of family. i doubt she did it because she wanted her child to have to get stuck traveling 10 hours every weekend.
maybe you and your husband could move closer to them.
i'm betting a 10 year old is way beyond 'starting' to be aware of the situation. he's the one who's been stuck in a car for half his weekends for as long as he can remember, going to stay with people so strict that it's making him throw up.
maybe you can duplicate just a little of his mother's 'laxness' (i assume that's what you mean) and make the young fellow feel more welcome. your imposition of rules and bedtimes is clearly not as reassuring for him as you want it to be.
if he's dreading his visits this much, i'd work on making my home a warm and welcoming place for him. he's only 10. it's not his to fix.
khairete
S.