That's correct, you still get Child benefit and Universal credit from UK government too. It's quite a bit more money. The forms are not as stringent either. DWP forms used to take me 7 hours. SCDP takes two hours at most. That is good thing if you are an exhausted parent who is short on time due to caring duties but it makes it easier for grifters. They still require supporting evidence from medical professionals and schools though. It's also at least a 2 year waiting list just to have your CAHMS referral looked at. The schools for children with complex additional needs are oversubscribed. I don't know if the situation is as bad in England but her son might miss out on vital help if she relocates.
If she does relocate, it's going to end up like guest and Leggy. When Bex inevitably gets kicked out on her arse, where will she and her poor son go? I imagine her parents won't take them in.