Do you have legal custody of your children? Your former spouse/partner has no right to them at all? If they do, then you will likely need written permission from them in order to send in the immigration applications for them.
As for your own immigration, are you qualified for any of the NAFTA professions that would get you a temporary (renewable) visa?
A professional must
be qualified to work in one of the more than 60 professions listed in Appendix 1603.D.1 of Chapter 16 of NAFTA (for example, accountant, computer systems analyst, engineer, management consultant and technical publications writer)
have pre-arranged employment with a Canadian enterprise in an occupation that matches the qualification.
You must also have a job offer from a Canadian company *before* you can apply for the visa.
Or if you're not qualitied specifically for a NAFTA type visa, then you could try for some other immigrant for skilled worker visa, which goes on a point system. You would also need to have a significant amount of available cash in a bank account, to show that you have funds to support yourself and your children while you are looking for a job. The amount for a family of 3 is $15,563 currently. And honestly, that wouldn't last very long if say, you choose to live in Toronto or Vancouver (I'm going to assume you don't speak french so won't be choosing Montreal!).
Here's the info about the point system for skilled workers
http://www.cic.gc.ca/english/immigrate/ ... actors.asp These types of visas can take a year or more to process. Like I said before, don't start packing just yet.
If however you are lucky enough to be independently wealthy and have more than $800,000 in the bank, you could immigrate based on an immigrant investor program.
Actually finding work in Canada will depend greatly on where you want to go and what you're qualified to do. The big cities will maybe have more options as far as jobs go, but cost of living is of course higher.
Job search engines for Canada are much the same as the ones in the US.
http://www.monster.ca http://www.jobshark.ca You can also Google the local newspapers for most any city in the country and check their Classifieds.
I will also of course suggest that if its just a new start you want and to get away from your ex, the US is rather huge itself, if you move to the other side of it, that's pretty far away as well. You don't necessarily need an international border between you. Several states might suffice.

Less paperwork that way. And cheaper! Canadian immigration fees are HUGE! For the 3 of you the fees will be well over $2000 for the skilled worker application for you and derivative for your children. Not to mention the cost of the move itself and all that goes with it.