In direct answer to your question:
NO
You must employ a European citizen.
Your girlfriend will have very few points to even get in the UK as a cleaner!
Training to be a careworker in the Phil is worth bugger all in this country, they have to start at the bottom and do an NVQ.
The hint is in the word 'girlfriend'. The only visa's applicable are Fiancée or Spouse.
And I personally think it's a bit sad wanting your 'girlfriend' to look after your ill mother, when it is your own families responsibility. I'd call that abuse, regardless of what she says, this is a strange country to any Filipina coming here, and it can be very difficult to adjust without being given the instant responsibility of looking after someone else.