Congratulations on taking your family's health in a positive direction. Welcome to the community!
To me the most pragmatic, no nonsense approach to Paleo is Archevore and its 12 steps - http://www.archevore.com/get-started/ . Just work your way down the steps as far as you can go.
I am also a very big fan of Perfect Health Diet ( http://perfecthealthdiet.com/ ), which for all intents and purposes arrives at the same place as Archevore on the core tenets of implementation (though some additional focus on supplementation)
One of the most accessible intros to Paleo on the web is the 9 part series by Chris Kresser - http://chriskresser.com/perfecthealth
But you are already on information overload. If I had to cut this down to the essence, the key area of focus initially should be toxin avoidance
- Avoiding gluten grains
- Avoiding vegetable oils
- Avoiding sugar excluding possibly some fruit
- Avoiding soy and peanuts (legumes)
By avoiding the above, you will naturally favor healthy animal proteins and fat, and vegetables including some safe starches such as potatoes/sweet potatoes assuming you are not starch intolerant.
Take it slow and don't worry about all the minutia you will read here and elsewhere. If you focus on avoiding toxins (as listed above) initially, the rest will fall into place. Good luck!
EDIT - I forgot to comment re: kids. For most kids, I think cutting down/out the sugar is probably the most significant change. Replacing the vegetable oils with good fats such as butter is probably relatively easy. The avoidance of grains for kids is pretty tough given the ubiquity of bread, pasta, etc in the diet of most kids and what is served at school.
This leads to another point as a newbie - don't worry about perfection right now (or possibly ever), particularly with the kids or it will drive you insane (it did for me at least). Progress, not perfection!