I have experience of both live-in care and care homes. My father had live in care for 17 years following a major brain haemorrhage which left him both physically and cognitively very disabled (unable to walk, loss of mental capacity - like a severe stroke. He did NOT have dementia or the particular challenges that poses). We continued the arrangement after he died in 2020 as my Mum was by then clearly not safe to be alone in the house. Her physical health and dementia deteriorated severely in May last year after a fall. She was cared for at home for about 2 months before we moved her to a care home.
So…
24/7 live-in care can definitely be an option. It is similar in cost to a care home, but can be more expensive if you need a second carer to cover breaks or help with hoisting. It worked well for my Dad when he had my Mum there as well. She could oversee his care, manage the carers and the house etc… As her health deteriorated - with what I now recognise as early stage dementia for last 3 years or so - having carers in the house who could also support her was invaluable.
For 1-1 care and attention - really personalised care - nothing beats live in care from regular, dedicated carers.
If BOTH your dad and your mum need support then it might be an option. Our set up was quite flexible. We would pay extra when occasionally the carers needed to be up at night . They worked 2 weeks on, 2 weeks off. They got a break of 3 hours proper non-working time every day. Aside from that their hours were flexible.
That said… it is hard work for the carers. Finding good ones is hard. Your home is “occupied” 24 hours a day. If the relationship gets tricky neither you nor the carer have any way to decompress like you would in a job where you work a shift and then go home. You are managing staff, even with a care agency involved. My Mum found it very very stressful at times, but to her it was worth it to have Dad at home.
It was much more difficult once it was just my Mum on her own, esp as she really needed a second carer for transfers, breaks etc. With no family near (I live about 4 hours away), and living in a big old house that needs quite a lot of maintenance, it just wasn’t sustainable for us. IF we’d lived close by then I think we would have continued it. But we were def in just waiting for the crisis to happen.
In your particular case I would worry about your Dad too. A respite stay in a care home
for your Mum so your Dad can have some recovery time sounds very sensible. Then if Mum is settled in the CH and your Dad is OK without support himself that may be the best option.