I can see similarities between your situation, OP, and my own family's - but from your youngest's POV.
There are 14 years between myself and my oldest brother. He and his family are NC with our mother/my father, but maintain a relationship (which is pretty close; he's the first person I turn to in a crisis, and I appear to be his) with myself and my children.
Our mother, however, blames the NC on my SIL, claiming that she "want(ed) [DB1] all to herself!" and so on. SIL did her utmost to maintain the relationship between my mother and DB1 - until she realised that it was never going to work. That my mother would always view her as "a mistake" and "not good enough" (my mother spent their wedding day trying to convince DB1 not to go through with the marriage!). DB1 went NC with our mother/my father the day after I turned 18. He says that he had to maintain their parent/child relationship until then, in order to make sure that I was safe, but that as soon as I was legally old enough, they were finished with my parents.
The fact that she called SS and reported you as someone who needed parenting lessons, is worrying. What has your youngest said to them? As for her hiding and avoiding you... well, whilst very immature, perhaps that is better than her telling you what she thinks of you? Maybe she - like my SIL - is of the opinion that if you can't say anything nice to someone, say nothing at all?
My mother refuses to accept/acknowledge that she is at fault anywhere in the breakdown of her relationship with my brother and his family (she has a grandson she's never met, and - if my brother has anything to do with it - never will!). Your youngest may well be siding with you... because they feel that they have no other choice, but to. I know from personal experience that at 11, I did exactly the same when questioned about whether or not I wanted a relationship with whichever relative had pissed my mother off that week. Children are loyal to their parents... until they realise that they actually don't have to be.
Encourage your youngest to have a relationship with their brother, communicate with your son, listen to what he and his wife - the woman he chose to marry and hopefully spend the rest of his life in marital/familial partnership with - have to say, and go from there.
Just don't make your 11 year old feel that they have to choose between you. Because, honestly, I've been there, as a child not much older than your youngest - and it's not a great place to be pushed into.
What is your son's relationship like with his other siblings, though? Do they get on, or does he feel like the black sheep of the family...? Could your DIL be trying to protect him from being hurt/herself from having to deal with the fallout of his emotional pain?
