You are being treated as an independent contractor. As such, you are responsible for paying your own taxes (income and CPP) and collecting GST/HST (if you collect more than $30,000 per year) as well as filing the appropriate returns. You have the ability to "write off" reasonable expenses involved in your business. If you collect GST/HST, you have the ability to claim back any GST/HST that you in turn pay out for business expenses.
But for the purposes of explaining this to CIC, you would provide them with a copy of your tax information. That's all they should require, they should not need to speak with your customer (she is NOT your "employer" because you do not have an employee/employer relationship.)
Here is a nice post for the rules regarding domestic workers (which includes "house cleaner") in Ontario: http://www.labour.gov.on.ca/english/es/pubs/factsheets/fs_domestics.php. I don't know where you are located, but odds are that there will be similar rules.
Note: if you really are an employee, then your employer has made a serious error because she is now liable for paying your CPP and EI obligations as well as her own, plus penalties. See http://www.cra-arc.gc.ca/E/pub/tg/rc4110/rc4110-e.html#employee_selfemployed for a description of the distinction. From your wording and the description you've provided, I suspect you really are acting as an employee and your employer is trying to "get away" without obeying the law - and this is being done at your expense.
If you are an independent contractor, then all CIC will need is your financial information - your tax filings with a cover letter from your CGA would be more than sufficient.
Now that I think about it, I am curious: why do you need to report this information to CIC at all?