Holly you are misled but its totally understandable why the info is not out there in any useful way.
How it works is this
You have a HB claim lets say for ease sake your rent is £100 pw as off the first of April this year £14 pw was taken off you straight away for 1 room over and above what they say you need. ( along with several other amounts for different things) now about 4 weeks before 1/4 a court case was won by some families with disabled children ( the case had already been won but was appealed by the LA) that basically stated if you have a disabled child the LA has to asses the case for exemption they do not have to do anything other than asses.if medical evidence can be provided that confirms the none disabled child in question ( or if both are disabled the one who you decide not to apply for leaving you another chance to apply if turned down) would create unreasonable disturbance to sleep.
If they don't exempt they do have to justify why not and it can be appealed.
So that's children done.
On to adults no such exemption exists so the £14 gets taken off your award however you can make an application to the DHP/DHF this is a time limited none long term first come first served type of fund.
They also do not have to follow the normal benefit income assessing rules so can take Into account income that is normally protected from means testing even if it is already committed to care costs.if they want they can decide to say "nope you can do away with your carer or xyz"
Its intended to be used for people at risk of homelessness short term to allow them to move to more affordable housing and is in no way guaranteed to be awarded no matter how valid your case is.
Different LA's can decide there own criteria for payments historically its never been enough one of its prior usages was for under 25's with estrangement problems after they changed the rules for those. Each time they change the rules they boost the DHP but never enough to cover the fall out.
Most disabled adults will get turned down unless they have professional help to apply same as all the other disability related benefits. But with the DHP there is no real challenge and no real rules they have to follow.