What does he want to do? Is he getting paid for watching the brother?

Not fair at all. He wanted to work and now he can't because he has to look after his brother ? No no. That's not his responsibility, mom should find suitable childcare not use his own son as free babysitter 

How often does Dad have custody of him? Is it enough where SS could work during that time only?

Not sure what country you're in, but in the US, 15 year old can only work a few hours a week (maybe 15?) doing very limited things during limited times. Even if Dad has a really limited schedule, it might be doable.

Ultimately, BM is CP. Is it fair what she's doing? Nope, but it's her prerogative. Your SO can only control what happens on his time.

I am on the fense on this one.  I am 6 years the elder and could have and would have happily been the baby sitter for my younger brother(s), paid or not.

My parents never asked me to baby sit or watch him.  Until I was in my early 20s.  At that point he was 14/15yo and mom and dad had a number of extended month or more business trips over a couple of years. I still did not mind.  Certainly he and his HS friends did not mind having his older brother "in charge" and out living his life on weekends while our home turned into the HS party palace.  The number of times I approached the house late at night after a night on 6th street and my radar detector would start pinging a mile or more from the house then be screaming when I pulled up to the house that had half a dozen police cars staged a few houses away in every direction to make sure none of the drunk teens tried to drive home.

I get both perspectives.  To babysit, or not to babysit your younger sib(s).  Regardless of the teens desires... this is the parent's call.

Id just pick him up and take him to work,  leave mom to worry about the younger one, that's that. 

I find myself wondering whether her telling him that he has to watch his brother all summer isn't just a knee-jerk reaction to her finding out that you were the one who got him the job ...

Who looked after the yss during previous summers?

I have a 16 year old with a license and a car and she desparately wanted a summer job.  she's been hostessing at TGIFridays full time all summer and really likes it.  I also have an almost  7 year old in two weeks. 

I paid for camp for her to attend every weekday from 7 to 5. 

I don't know, 15 is a tad young.  Maybe your DH can ask BM to give him a small paycheck for watching his brother? Families help eachother out-it's not like a case of a 17=18yr old watching her siblings all day.  This is during the summer-and if it's her custody time you have no choice but to respect it.  There is nothing wrong with kids given the responsbility w/their siblings once in a while or for a summer. Maybe the mom would be willing to pay him what he would earn if he worked?