Both Norway and Iceland are very expensive. You can of course do them cheaper but some sacrifices need to be made which may or may not work for the entire family.
WOW airlines bag policy is ridiculous; a year or so ago they provided a tremendous value now I am not sure I would ever fly with them ; their return flight home rates have gone up and by the time you add the basic services the other airlines provide the cost is often a wash if not higher between them and Icelandair or Norwegian.
I know many people that do Iceland on the cheap but they eat the food from grocery stores and at the gas stations, hot dogs, snack/junk food basically or in the summer might rent a camper van and stay in the various camp ground facilities.
Time for Iceland really depends on what you want to see, most recommend a full week if you want to see Reykjavic, drive the entire ring road. Otherwise with less time (and I think the stopovers are limited number of days less than 1 week) then you have to pinpoint what you want to see as your plan will involve driving to the furthest point and then back from where you came, as the circular ring route you likely don't have time for. Of course since you will have near 24 hours of light in the summer some will sacrifice more sleep than usual and travel further each day.
Giving numbers is near impossible because their are options at all price ranges.
Stating things in nice restaurants cost double is probably a good reference point ; when I say nice I am thinking of your average in town, sit down place not an overly fancy affair. Often brought up is the high cost of alcohol ; and it is true alcohol costs close to triple what it does in the US but for a family vacation I cannot imagine that really matters in the grand scheme of the trip/overall budget. if you really love beer though, expect at a hotel to pay between roughly 15 USD for a pint. Norway seems to have a good regional microbrew culture.
Gas will cost a little more than double. Car rental daily rate is a little more than here in Norway ; in Iceland a bit higher plus they seem to make a good amount extra on insurances which most opt for. Norway seems a little better for rental cars overall and I also believe Iceland in the summer is so popular right now (the cheap flights are a major reason) that car rental availability will book up quickly. Sweden and Denmark I believe are less expensive than Norway for rental cars and most everything else as well.
Since you posted this on a Norway forum I assume you are very interested in seeing Norway. From Copenhagen driving it would be hard for you to visit more than just the most southern sites in Norway though. If you are asking what would interest me the most, I would have no problem entirely skipping Sweden and Denmark and spend your time in Norway.
Norway is really big (tall and narrow) and traveling around it often requires domestic flights (not just driving) to cover a good amount of it.
As I recall a pilot stating when we were flying into Oslo that shocked me, Oslo is closer to Rome than it is to Svalbard, Norway.
Lodging all depends, should be able to find reasonable places on Airbnb ; for a party of 4 hotels are likely not going to come cheap outside of very basic ones
