HELP?! American and Mexican - how best to go to Canada?

Greetings. There is some good information, but I have not seen a situation exactly like ours, which is pretty impossible.
I am an American citizen. My spouse is a Mexican citizen. She was in the US illegaly, which is where we were married 8 years ago and had 2 kids together. We tried to fix her immigration status and it got denied so far though we are continuing to follow through with reconsideration. This process could take a while though. Now that my family except myself is Mexico, I visit them when possible, but this really isn't good enough for our family. We need to do something to be together while the US is processing our case. Mexico really isn't an option as I wouldn't have any means of supporting us. I live pretty close to BC so that would be the area we would be going.

I do not want to apply for permanent residence in Canada yet because it could invalidate our case for me sponsoring my spouse in the US, as I would no longer be domiciled in the US. If we end up losing the US immigration case, the I would probably apply for permanent residence in Canada, and should be eligible with a FT job offer.

Now that Mexicans need a visa to get into Canada, we have to explore the options.
I was thinking about applying for a temporary work visa. I have 2 jobs right now. I am seeing about getting a transfer from 1 of my current jobs to Canada, but I am not high enough on the manager pole to do an Intra-Company transfer without the LMO. Also it is not a FT job, it is 24 hours per week. I am planning on keeping my full time job in the US by transferring close to the border, so we can actually earn enough money to support ourselves in Canada.

My questions are:
1. Will I be able to apply from the US though my spouse is in Mexico?

2. Will our process take longer? Are there extra steps because of our application being for 2 different nationalities?

3. Will the US immigration issue be scrutinized at all? Does the illegal stay in the US transfer to be considered having commited a crime for Canada's purposes?

4. Would it be better for my spouse to apply alone to visit a friend that we have living in Canada (on the other side of the country though) or to apply alone rather than me applying for all of us? I have thought of this because my kids and I can just go there to stay temporarily and I wouldn't have to get a new job (or transfer) in Canada.

I'm sure I will have more questions. Please feel free to offer any suggestions. Thanks to anyone in advance that can help.