Hi Janand
what a time your family are having
you are the ones who know your mum best, and know how advanced her dementia is, as to whether or not she can give informed consent, and what her wishes would be - she will, though, definitely need appropriately talking through what is happening to her at every stage, especially if she forgets, as she will have to deal with what has happened to her body and the healing process
I had a full mastectomy and removal of lymph nodes several years ago, and it is a big procedure - because mine was 'full' I didn't need any follow up chemo or radiotherapy, I took pills for five years after instead - I healed well, though and the chest area didn't cause trouble, just felt odd
I hope the GP will give you lots of info - and do contact the Breast Cancer Nurses at the hospital, they were a great comfort to me and I'm sure will pay special attention to your mum's needs - they will be able to give you considered and knowledgeable information - maybe link in with an Admiral Nurse if there is one in your area - possibly also talk with your local hospice as they will have experience of these complicated issues
I'd also suggest you ask for a lot of support when she comes home - maybe even consider that she recuperate in a nursing care home so that help is 'on call' all the time
your dad must wonder whether he's coming or going
I wish you all the very best outcome