My mother is 99 years old
My goodness you have to much on your plate. If the care agency has a problem it’s up to SS to sort.
Make sure they get involved and take responsibility!!!.
Regardless of age - age being no bearing on anyone being constantly difficult.
Find out the bottom line re:withdrawal of care at home. I would suggest the next step would be residential.
Discuss this with you mother. She has one option except the care gracefully or residential.
At that age, some sort of dementia type illness, or mental decay, is very likely.
She probably doesn’t fully realise what she is saying. It SOCIAL SERVICES cannot find any carers, then SOCIAL SERVICES need to make alternative arrangements. Don’t let this get dumped on you, it is their responsibility, not yours.
YOU cannot be forced to care.
I would suggest that she may need an “EMI” home, i.e. Elderly Mentally Infirm as that would be the only place which would be able to manage someone so unpleasant.
It’s horrible to contemplate, I know. What matters now is what she NEEDS not what she WANTS.
Recently had this situation. Felt obliged to give finding a personal carer through direct payments a go. Working out better than agy but as could only find one for five mornings meaning I am having to do more. Not sure how sustainable that is if am honest. 
Many thanks to those of you that have responded.
In that case, get your phone out, record her when she is shouting horribly at you, to use as evidence. THEN WALK OUT. You do NOT have to put up with this. Do not give her warped mind an opportunity to delight at your discomfort or distress.
You are not her “little girl” who has to put up with it. She needs you, you don’t need her. Maybe point this out to her??
I agree it’s terribly sad, if I were you I would have given up trying to help her long ago, because love is a two way street to me. If you love her enough to care for her at the age of 99, she should love you enough to be civil, at vey least!