Typically chassis batteries are not charged from shore power.
"Typically" does not apply here - it is simply a feature difference among brands and models of RV. All Fleetwood Class A's, including the OP's American Eagle, do indeed charge the chassis battery(s) from shore power. Some other brands may not, or provide it only on selected models.
he solar charger has nothing to do with it. Your coach has a battery control center (charge controller) that closes a relay to enable chassis battery charging once the house batteries are adequately charged. If the house batteries do not reach a certain level, the relay may never close. Or the controller or relay may have failed.
If you can't find the problem, it is a fairly inexpensive fix to add an auxiliary charger called a Trik-L-Start