Copenhagen to Stockholm with children

Preferred airline from Chicago to Copenhagen?

SAS. It's always nice with direct flights. And they fly Stockholm-Chicago as well so you can book an open jaw ticket with direct flights both ways.

Should we stick to Copenhagen and Stockholm with our minimal number of
days on the ground? Or should we plan a stop along the way from
Copenhagen to Stockholm?

7-10 days will let you see Copenhagen and Stockholm without it feeling too rushed. So there is certainly time for a stop along the way if you want to , it is pretty easy to do without loosing to much time. Eksjö could be an option, a small town around half way between Copenhagen and Stockholm with a cute old, mostly wooden, town centre. A bit more out of the way is Visby, that is well worth a visit.

Should we try to include Norway?

That would in my opinion make it a bit too rushed.

Toddler friendly accommodations?

Shouldn't be too hard to find.

With a 2 and 4 year old, I'd seriously consider veering slightly off the main train line to Vimmerby for Astrid Lindgren's World. I'd spend a couple of nights in the area for one full day at the park, best if it is not a weekend from what I hear. If you haven't read the books to your children yet, you have plenty of time to do so before your trip. Pippi Longstocking books and Emil books is where I'd start and move along to the others as time allows.

True, Astrid Lindgren's world might be a good place to stop if it's something that can be of interest for the children.

The Scandic chain has many family friendly hotels.

7-10 days would limit your plans. We spend five days in Copenhagen prior to a cruise and loved it.
On another trip, we stayed in Stockholm and took the train down to Copenhagen (nice train ride) then took a 11 day Norway Arctic Circle cruise.

Stick to Denmark and perhaps add Stockholm.

Norway is amazing, suggest a cruise up the coast. Do on another trip.