It will be very difficult Joy. Adult dependant visa is expensive and the most difficult to get. You need to have proof that no one else will look after her in the Philippines which will be difficult since you have your sister there. I believe your mother is also well able, healthy and can look after herself so chances are very low.
"My wife has been looking for a live-in helper to stay and care but still to no avail. My wife will stay and train and see if she can trust and leave the helper." Not a good sign that... As someone else said get in contact with a professional agency (I mean you get in contact with them - not your wife) - ask the agency to assess the situation - how much care mum needs etc. and the expected monthly cost... If your wife isn't open to that then you've got another kind of problem.
Maybe it'll be an option someday when I have a stable job here or when I become a permanent resident. Hubby may not want it anyway lol