Sounds like quite the trip. You don't mention whether your teens are outdoorsy or in any way what they like. A long period in a car or even RV would be best spent with people with good attitudes, so hopefully they are up for a road trip with occasional limits on internet access and that might need some inquisitive minds.
If I were to pick a route from southern California back to NY, I might wind my way past:
- Kings Canyon/Sequoyah
- Grand Canyon
- Mesa Verde
- Rocky Mountain NP
- Badlands/Mt. Rushmore
- Chicago
- Either upstate NY via Pittsburgh or southeast through WVA and VA then up through DC
The key will be how much you want to drive each day. The goal should be to be stopped as much as possible somewhere interesting. Map it out so that you don't get stressed out having to make it somewhere that night. With several stops, you are probably looking at a minimum of 60-75 hours of driving over 12ish days, so consider that.