So, 11,500GVWR truck with a 21k GVWR trailer hauling your crawlers around for recreation (ie: not racing for money)?
Digging a little, it looks like CA does not allow a "Non-commercial Class A DL" to tow trailers over 10k GVWR (other than RVs and livestock trailers) per:
https://bchcsjsu.org/uploads/3/4/7/0/34706757/chp.pdf
And the CA flowchart linked to earlier updated for your use case:
https://www.chp.ca.gov/CommercialVehicleSectionSite/Documents/Driver License Flowcharts.pdf
So, the Yuba City DMV was correct, the Grass Valley DMV and the CHP Officer were incorrect.
Your options appear to be either get Class A CDL, or drop down to a 14,499# trailer with more pin weight (to keep under 26k GCWR and not need anything special for a license).
One of the "2 day CDL schools" such as:
Ozark CDL, LLC - Services might be your best bet.
Aaron Z
Edited to correct my misconception that a Non-commercial Class A DL could tow a 10-15k trailer that wasn't a RV or livestock trailer