Your sponsor is obligated to provide for you for 10 years after you land - if s/he doesn't, and you collect social assistance, s/he is obligated to repay that to the Canadian government. They cannot send you back to the West Indies if you already have PR status. You are a Canadian permanent resident and, as such, you have the right to live and work in Canada as long as you maintain your permanent resident status - which means you have to live in Canada for two years of each five year period.
I don't think there's anything you can do to force them to continue to support you in their home - especially if you are not abiding by the "rules" of the house. You don't say how old you are now, but if you are living under their roof, you should be respecting their authority - whether they can "legally" send you back to the West Indies or not. Maybe your family can get some counseling to work through some of the problems it seems you might be having. Family is a terrible thing to waste.