Hello and welcome to TP, you will get lots of help and support on here
Goodness me you are all managing with so many difficulties.
Sounds as though both your parents need help. Hopefully you have Attendance Allowance for both of them? This is non means tested and really helps.
The social worker will be trying to find out how much practical help they need in the home to keep them safe mostly centred around care packages in the home - so do they need help in mornings to get dressed, washed etc (personal care), do they support with meal times and do they need help getting to bed at night. They can also help your parents access a lunch club or day care centre - very useful.
Worth asking if there is an Admiral Nurse in your area (dementia specialist nurse)
Hopefully they will arrange an occupational therapy assessment before your mum comes home to see if there are any aids that she needs in the home - grab rails by the front door, maybe a perching stool in the kitchen, perhaps a trolley to get things from one room to another and some bathroom aids. Hopefully they will also look at what they can help your Dad with.
If you are already or are planning to support them then you can as for a carers assessment which would give you some free sitting hours hopefully to have a break from caring - or if your Dad is looking after your mum then he should have the carers assessment.
There is also a council tax waiver for someone with mental impairment which includes dementia.
Come back and let us know what happens. There is a LOT of help out there and we can give you more signposts - Age UK are very helpful with filling in forms for things like Attendance Allowance (do get help, they are tricky)
Alzheimers Society have a dementia helpline and can give you all sorts of local info
Your local carers organisation will have info on carers cafes where you can get a lot of local information over a cup of coffee.