Canadian with TN-status living in the US - 2nd job

[Mathew]

Hi,
I am a Canadian working in the US with TN status.  My sister who has a consulting company needs some work to be done in the US.  Since I live here could I go do the work for her in the US facility under her company name?  The US firm will issue the invoice to the consulting company in Canada.  In turn my sister will use my Canadian SIN to pay me as her employee and I will pay taxes in Canada (even though I reside in the US).  Is this legal?

Also, as a Canadian consulting company would you know what the US company needs to file for tax purposes?

Sorry that I am so clueless.

Your help is sincerely appreciated

Mathew