traveller2 wrote:My husband has been granted a H1-B visa. My current employer in Canada has (very graciously!) indicated their willingness to try out telecommuting for me. I would be physically working in Canada for one week per month but remotely from US for the rest.
Where you are when the work is performed is what matters for immigration purposes. You cannot work on H-4, simple as that.
Note also that you would be liable to US
taxes on the income you earn while working in the US, which would require your employer to have a US payroll and you to have a social security number, which you can't get on H-4. So you can't really fudge it or lie about it on an on-going basis, if you did you or your employer would run into problems with the tax authorities. Even if you did you would be considered resident in Canada for tax purposes which may not be a good idea if your husband works in the US.
You certainly can work in Canada, nothing changes in that regard except for the fact that you become non-resident for tax purposes (if you want, depends what your husband wants to do), so you would have to file a new TD-1 with them so they withhold the correct amount of tax and you would only report Canadian-source income on your T1 (i.e. what's on your T4).
There is no work authorized category that allows you to do this, unless you can get an open-ended EAD, for example if you were J-2 or L-2, but your husband would have to get J-1 or L-1. And it doesn't solve the problem of your employer having a US payroll, although if you had an EAD you can be self-employed and do payroll yourself and invoice them.
You don't qualify for E because of the lack of an investment so the only real method is for your husband to get sponsored for LPR status, then you can get it and start work. But that is a long-term solution.
Steve.