Re: I hope I'm not too late...
You can move to Canada whenever you want with your household goods and pets. Your husband and children will have to be sponsored to immigrate to Canada. However, they can come to Canada as visitors while you are waiting for their applications to be processed.
If I were you, I would move up with my goods and pets and get settled. Then have your family come, telling the border officials they will be visiting. Americans ordinarily have no trouble getting in to Canada, especially the first time. They can stay for 6 months, and can apply to extend this time.
If they wait until you have already submitted the PR applications, they can bring the proof of payment with them to the border, and they will then get a visitor record. For Alberta, this means they may be able to get provincial health insurance quickly; each province has different rules for this. I would not do this; I would just come first, and have them cross the border separately. Filling out the forms can take quite a while.
Your kids can go to school, but they will need a study permit and may have to pay international school fees, which are high. Some forum members have reported that the school officials in their area did not require this, though, so it's best if you check with the school division where you will be living.