If the only outcome from the previous assessment was a handrail then it sounds like an occupational therapy assessment not a social work assessment. Even if a social work assessment was completed then it can be done again if things have changed and your dad could also have a carers assessment just for him.
Even if your mum will be self funding her care (does she personally have over £24k in savings in her name or a high income - the house won't be taken be taken into account if your dad still lives in it?) then social services can still be involved if needed - they aren't just there to fund care homes they can assist with the practicalities as well in complex situation like this.
If your mum does go into care then she will be subject to a Deprivation of Liberty order (DoL) which will be applied for by the care home and agreed with the local authority and the court of protection if required. If your mum does require any of the mood calming medications then this will be agreed with the local older adults mental health team and included in the DoL.
When was she last reviewed by the Older Adults Mental Health team and are they aware of the aggression? Most sedating medications such as Lorazepam are only prescribed on an 'as needed' basis and are reviewed regularly, so it would only be given if she was having a particularly agitated day and your dad could/should discuss this with the mental health nurses in much the same way a care home would if she was with them.
Carers are specifically included in the legislation for Safeguarding because it's recognised how vulnerable their caring role leaves them to abuse from the person they care for and how few options they can feel they have to change the situation.
I regularly get involved in these kinds of situations where it no longer becomes manageable and the risks to the people involved if we don't intervene outweigh their right not to have state interference. These things rarely get better if left alone they usually get worse and end in a crisis admission to hospital / care homes/ mental health ward. The earlier professional are aware of the situation to try and help reduce the risks the better.
The current carers will also have a professional duty to report to adult social care if they witness or become aware of aggression towards your dad.