Live-in can work really well if someone needs a lot of help. It can be cheaper than having someone just during the day. You get the continuity and flexibility of having someone around
The carers will help with any and all household tasks - everyday cleaning, laundry, shopping, errands, cooking. All the things your Mum would do but can’t. Ours never did gardening or maintenance/odd jobs so you may need to arrange separate help for that.
They need their own bedroom in the house. Ideally one which can fit a chair and a small TV too so everyone can have a break from each other
Typical working pattern might be two weeks on, two weeks off, with two careers alternating. You will need holiday cover too.
They will also need time off during the day. I think ours had 3-4 hours each day. So long as you don’t need someone in the house literally 24/7 - ie your Mum is OK on her own for a few hours, can get to the look by herself - that’s fine. If not you would need another carer to come and cover those hours
They aren’t expected to be awake at night. If you need someone to watch overnight you need to ask about “waking nights”. Again might mean an extra carer.
Ours were happy to cover occasional nights(eg if someone was ill) and breaks during the day. We paid them for the extra hours. It saved arranging separate carers
If any tasks need two carers to do safely - mainly applies if someone needs a hoist for moving - then again an extra carer needs to come in for that time.
I’d recommend starting with an agency who will take care of all the employment admin, finding people etc… Although long term employing directly will be cheaper. It’s similar cost to a care home, and if one carer can look after both of them in their own home, may be cheaper right now .
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If you end up with Dad staying in the care home, and your Mum just needs a bit of support rather than personal care, you into the Age UK scheme where you get a live in lodger who can do a few hours a day of things like light cleaning, errands and cooking. They don’t do care though - eg help with dressing, washing