There are several issues here. Firstly, the statement that "Access arrangements are for a parent to spend time with their child, not to provide childcare for the other parent. If DH is not there, then why is DSS?" doesn't ring entirely true as this is not an "access" arrangement it's a 50/50 parenting split and as such this house should be as much DSS' home as his mother's house. And based on a 50/50 arrangement I certainly wouldn't be expecting there to be a rigid agreement that the child is only with one or other parent when that parent is there, I would expect there to be some times when the parent is not there and the step parent be responsible for the child. That being said, those kind of arrangements do need to be discussed between the parent and the person they expect to be there when they are not, and it sounds as if the OP's DH has unilaterally changed his work hours without actually discussing this fact with his partner, and at the same time maintaining the nights his DS is scheduled to stay there.
OP your DH has been incredibly selfish in unilaterally changing his work hours without talking to you about it, especially as you A, are still expected to be responsible for his child during that time, and B, you have children of your own who demand more of your attention and he should be there to help out with those children as well where possible. With regard to the ex, she absolutely shouldn't be sending you texts and i would make it clear to her in no uncertain terms that this is to stop or you will be forced to speak to the authorities. However, from her point of view I would imagine that she is somewhat pissed off about the fact that her ex took her to court for greater access and doesn't actually spend that time with his child, so clearly he did it to prove a point rather than because he wanted more of his child in his life.
At this point you need to speak to your DP and tell him that this just isn't working with his child being there when he isn't, and that while 50/50 is all well and good, he needs to speak to his ex in order to come to an arrangement which suits them both.
WRT the child, twelve year olds can be notoriously stroppy, but you have to almost treat them like toddlers, and ignore the bad behaviour, reward the good behaviour. So if he's behaving like a stroppy teen I would give it no attention what so ever. He will soon learn there's nothing to be gained if he can't get to you and his behaviour creates no response. And if he goes off to his bedroom, wel let him. Don't worry about whether he speaks to the baby, twelve year olds often don't engage with babies even if they're their full siblings. Again just ignore ignore ignore.