Nah, YANBU, and don't feel "guilt tripped" by a few posters.
What happens if he doesn't get into university?
Do you think he'll still resist going to his parents' home?
Is his sister making new friends there?
Is it the Republic or NI they moved to?
(Curious as to how it affects fees / loans)
re "doesn't even like going into a shop on his own!"
I went off to college at 16 and was living in digs. OK, I was effectively getting bed, breakfast, (and evening meal most days Sunday-Thursday), but had to quickly keep track of cash, timekeeping and while there was spare time after a 9-5 college day, there was a curfew as I was fairly young!
If he's thinking about university, he'd probably learn a lot with VSO, work for free in a charity shop (as it's not all about money), or do something else "real world" where he's expected to be in on time, accept whatever the "boss" tells him to do, and muck in with the tea run, getting his own lunch, etc. and fend for himself when he's not working.
Perhaps if you are going to allow him to stay on until September, you tell him that cooking will be one of his tasks (with some tutoring from you!) plus general cleaning, bedmaking, etc, as it sounds like he'll benefit from the knowledge when he does get to Uni.