What have the council actually told you OP?
What department have you spoken to? Allocations? Or Housing Options?
The reason I ask is that some council decisions can be challenged. if you can say what they have actually told you then I can offer some advice as to what your options are both legally and other ways you can possibly get help to move.
Would need to know your local authority so I can look through their allocations policy for you.
Bear in mind, that most councils will count a living room as a "bedroom" so even if you are successful in being moved, you may still only be entitled to a one bed property as children under one are not counted for bedrooms so you could even only be entitled to a one bed when your child is older. Some authorities have more generous allocations policies though.
If you are being harassed by your dad and are in danger then you may be considered legally homeless and so you could make a homeless application if you have not already done so. If accepted the council will have a duty to house you in emergency accommodation whilst they decide if you are owed the main duty.It's pretty bumpy very unsettled route though.
If you are owed the main duty, then you would be given temporary accommodation and you will be given 1 offer of permanent accommodation that could be anywhere in your borough. If you refuse, they will end their duties. How long you are in temp accommodation would depend on the pressure on housing stock in your borough.
For instance in London it is not unusual for people to be in suitable (?)temp accommodation for years before they offered something permanent However, in my area people are housed permanently within a few months.
You can apply for priority on the waiting list if your medical conditions mean your current property is unsuitable but you will be expected to bid borough-wide otherwise you will lose your priority.
To have more choice in the sort of home you wish to live and in an area where you want to- you would normally look for private rented but of course you will not have such a secure tenure as you would a as secure council tenant.
Tough situation for you but possibly tougher options to think about.