Family Sponsorship would need either you to be married legally, or common law - which requires living together for one year.
At which point , in either case , you will need to decide to apply either outland, where you wait the process time in your own country
or inland, where you stay in Canada and wait the processsing time.
Outland has a possibility of you visiting , and extending your status as a visitor while you wait , though I am sure it would be tricky as you have children
and I am not sure how they would be able to go to school, as well.. you cannot work while applying outland, nor do you have access to health care unless
you play out of pocket as far as I know.
Outland applications are faster in most cases.
Inland , you can work after 4 to 6 months *not sure exactly how long* when you apply for an open work permit, I do not know how the enrollment of kids in school goes, and
I am not certain about health care in the various provinces.
Inland applications are long and take usually at least 2 years.