social services are trying to put my mother in a care home

To be brutally honest, its your feelings that are against your mother being in a Care home.
As you work, and have 4 visits a day, there will be times when she is alone.
4 doubled visits, is usually accepted as the limit of "at home" care. Once more than this is required, then Residential Care is the better option. Staff available 24/7, specialist equipment, etc.
As you say, you will not get the full spending package you feel you need to continue.
Now is the time to be choosing the right home for your mothers needs.
Usually a list of suitable places will be provided(that also accept LA funding) it's your job to pick the best suited.
Go see them all, do not give warning that your coming, just turn up, good ones will be happy to see you, not all will have immediate space, and you may have to go on a waiting list, for your chosen ones.

Your mother will not agree to go. They rarely do!! If you wait for an emergency situation to arise, you will have no say in what happens, when or where.
This needs strength on your part, to get the best for your mother.

I speak from experience, as do many others on here.

Bod