I have a close friend with Aspergers (properly diagnosed btw) and he really does need a list of what to do and when, a script, his wife calls it.
He is totally unable to use initiative and if 'put your plate in the dishwasher' is not on his list for Friday, despite it being there almost every day of his 27 year marriage, he doesn't do it.
I fail to see how Luckygirls 'carer' got her job, doesn't the agency screen people at all?
They could be sending out axe murderers (always my mother's fear when she needed home help). 
I hope you go ahead with the local agency assessment at least, then you will at least know, if push comes to (over the cliff) shove, what they're like.
Just as a matter of interest to no one at all, what she is paid per week, is quite a bit more than I have to live on each month.