My suggestion would be for you to first get a copy of Mark's guide for Alberta Paddlers.
In this guide, Mark covers much of the Alberta portion of the North Saskatchewan River. I have not paddled the very first section of your route starting at Saskatchewan Crossing, however, my understanding is that there are one or two mandatory portages in the reach before Abraham Lake that you will have to do. Abraham Lake through to the Bighorn Dam is a fairly long lake that is subject to strong winds. My favorite reach starts just downstream of the dam on the Forestry Trunk Road near Nordegg and continues into Rocky Mountain House. I have paddled the entire section of the NSR from Nordegg into Edmonton with my own family, when my daughter was about 3 yrs old. If you have paddling experience and use caution, this is a very enjoyable trip and quite doable for a family with young kids. I am not familiar with the section downstream of Edmonton, but that is also covered in Mark's guide.
have fun.
dave