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You cannot apply for permanent residency status on the grounds that your mother needs you.
You need grounds such as being a skilled worker, for example.
You can come to visit for up to 6 months and then can extend your stay further perhaps.
But you cannot work as a visitor.
It seems like the fastest and best route for you to take would be to get a temporary work permit.
You will need a job offer first.
The way it works isn't really that complicated.
What has to happen is this:
Your potential employer has to apply to the government for what is called a Labour Market Opinion (LMO). What this entails is the government reviewing the job market to ensure that there is a shortage of Canadians to fill your job. You cannot take a job away from a Canadian. So, you have to have a skill, or work experience, in an area where Canada needs workers and there aren't enough Canadians who have that skill or work experience.
If that's the case then the government will give the employer a positive LMO.
Then you can apply for the work permit.
You will need to prove your credentials and also need to undergo background, medical and criminal checks.
If all goes well you will get the permit.
Here's the webpage that has all the information you will need including the forms and information about the fees:http://www.cic.gc.ca/english/work/index.asp
Let me know if you need any further clarification.