I don't know how to vote. What is your reasonable/unreasonable thing?
Yes having a child with additional needs will likely get you more points, as a homeless person you'll already be in the highest banding. The refuge is officially temporary accommodation, regardless of how long you stay there.
How long it takes to get housed depends on a number of reasons. On a personal level, anything that limits your options means it could take longer. That could be things like: needing a ground floor property for accessibility, being unwilling to move out of the area you're currently housed, being unwilling to accept a council-assisted (ie they pay the bond and find a landlord who'll accept someone on benefits etc) private rental, holding out for a house rather than a flat, wanting to only live in a certain part of town. Or a myriad other reasons.
Luck also plays a part. You could bid on a property and even if you're not an especially favourable candidate for it, if nobody else bids it's likely you'll get it.
The main reason for whatever the length of time is for getting permanent housing, is the level of demand in your area and the availability of housing. In some areas you could he in temporary accommodation for decades. That doesn't mean you'll be in the same place all that time. They can move people to other temporary accommodation.
You won't be able to stay in temporary until your ideal property comes up either. Temporary is expensive and there's limited space, so the council wants people moved out ASAP. Eventually, if you're unsuccessful with bidding, they'll allocate you somewhere. If you're a decent person, keep bidding each week, look after the place you're in, don't cause problems with your neighbours, stay in touch with your keyworker and the housing officer and generally do everything you're meant to do to try to fix your life up as best you can - that'll happen sooner than if you're a PITA, rude and disinterested, always causing trouble with others, complaining about minor things or things nobody can realistically change, slowly trashing your current place, refusing to stick to the rules or stay in touch with those who are trying to help you and falling off the radar a bit.
If you're someone with options because you've got a half-decent job and are trying to decide whether to stay and wait for hopefully a permanent housing association place or whether to look for another private rental, I'd say consider things like how permanent your job is, your future employment prospects and your general financial circumstances. If you're up to your eyes in debt, your wage is only reasonable because you're working 50 hours a week, you've a history of being in dead-end minimum wage jobs and little prospect of that changing - then I suggest you'll be better off staying where you are. If you're unhappy with the housing you eventually end up in there's nothing to stop you private renting at that point, but if you give up the opportunity now it may never come round again, unless you're unlucky enough to find yourself homeless for a second time.
You can stay on the bidding list if you leave for private rental, but your priority status will change once you're adequately housed. Many people in these circumstances will never ever be housed, despite being on the list for decades. Be aware the length of time you've been on the list is something that's taken into account when allocating properties. All else being equal, the one who's been on the list longest will be offered the property first.