This may not be a popular suggestion, and it is just that, a suggestion, but have you considered a specialist school for your son? If you live 5+ miles a way from a the nearest town, a weekly boarding school might suit? One that has a good SEN provision and/or a very structured evening. They may be taking enrolments for Yr 9, a natural time to start. There may be special funding or a good state boarding school if money's tight.
How long does it take your daughter to do her homework? Could you enrol your DS in an after school activity that allows her some peace and quiet?
Will audio tapes help with his reading? Are the books prescribed or can you choose them- fun books might help.
He has challenging behaviour but is he okay once the homework is out of the way, or does the next thing become an issue? Does he do his classwork? It might be worth having a tutor, although if your DD1 can't help, I'm not sure if this will.
Alternatively, maybe if your DD2 doesn't come home until he's finished his homework? This might be more viable if you lived in a city, but even if its just one night a week, does she have any friends nearby (or an aunt, maybe) who can take her for a few hours?
Is it possible for him to stay at school until he's done his homework? Maybe the school library is open a few hours? A teacher might be willing to help? I guess if he's only 12-13 you can't actually just leave him there until he's done the work though, and did you say lunchtime aren't working?
Is the x-box his or does the whole family use it? If it only belongs to him, try locking it up until he does his homework, maybe?
Finally, a psychologist or psychiatrist might be able to help, but I don't have any experience with that so I can't recommend anyone.
Sounds like you have 2 very lovely and successful daughters and I hope that will a bit of help your DS will be the same.