You must include them in your PR application but you have two choices, to list them as accompanying or not accompanying but if you want them to join you in Canada now, it makes no sense for you to list them as not accompanying because it just means time and cost to sponsor them later. They will in both cases have to have medicals.
If they are accompanying, they get their PR visas at the same time as you and can land at any time after you have landed or at the same time. I assume they will mail all the passports with the visas to you. You can then make a trip to Nigeria to pick them up and you will all land together on your return with them or you can land earlier by going to the US and coming back from there or seeing about making a landing appointment at your local CIC office and then mail them their passports and they will come later.
To get the PR visas for the children, you need to show that you have full custody of them or that the other parent approves of you taking them to Canada.