I'm sure you've found lots of info on the Internet, so it's really a case of fitting things to your interests.
If you're planning a visit to the DMZ then I'd suggest visiting the war memorial museum before that as it helps put it in context.
There will be some baseball play-off matches going on late October. Not sure how easy to get tickets, but probably an interesting experience if you can.
If you like the historical stuff I'd visit Changdeokgung and Changyeonggung palaces as well as the more famous Gyeongbokgung. They should be lovely at that time of year as Korea is great for autumn colours. Might not be interesting for kids. Check if there any special events going on at any of those places.
The areas between these palaces are good for wandering. Bukchon Hanok village is most famous. Insa-dong is a nice artsy area nearby
There are food classes like how to make kimchi that quite a few people do.
Nice views from Namsan even if you don't go up the tower, and as mentioned already, nice autumn colours.
Do a bit of research about the food. The kids might not like the spicier stuff though.
The kids might like the Hongdae as it's very youthful, though geared to college age students.
The alphabet is actually really easy to learn phonetically - can literally be done in a day. Korea uses hundreds of borrowed words from English so you'd have an instant vocabulary to recognise.
Might be able to add more if I know more about what you like as a group.