Stay positive but come up fighting
This is definitely a hard time in your life, I don't think life can throw anything worse at you than a loved one with AD. My mum was 57 when she was diagnosed, after having been told from the consultant we should be grateful it wasn't a brain tumour which was their first impression.
Anyway my mum went into nursing care last month which was a very hard step, she'd spent time in hospital first, then back home and then into emergency respite because my Dad couldn't cope. He has Vascular Dementia which is very similar to AD but with a more stepped decline as I understand it.
With regards to your mum being in hospital, you definitely do need to shout and very loud. I've pushed ever since the day we knew what was wrong to make sure we had all the help we could get. Help to cope every day and also things that would give my mum stimulation. Make sure you have a good CPN (Community Practice Nurse) and if you're not happy change to another one, you'll need a social worker who also organise a care package for your mum. In this world you don't get anything unless you ask for it. I've found my local Alzheimers branch extremely useful they've advised on what services we are entitled to, when to push back on decisions and to also make sure we had all the benefits mum was entitled to, so we could pay for the extra services. I would push to get your mum out of hospital as fast as possible. My mum hated being in and had a few falls which have never happened before, they put her on new medication which helped with some areas, she was in for 5 weeks and we fought to get her back home as it wasn't a priority for the hospital. Again we couldn't have done that without the great social worker we had.
My only advice is to shout for action, get advice on what should be happening and read as much as possible on how to work with AD on a day to day basis. At the end of the day you are the only one who will make your mum a priority. Once you have things in place it does make you feel a little more comfortable and show that there's light at the end of the tunnel.
Take care and stay in touch.