A Southwind definitely does have bi-directional charging (a battery charge controller or BCC). Probably an RV Custom Products module in that coach model. Whether the new converter is properly connected to it is anybody's guess.
In the usual Fleetwood RV design, the house (Aux) battery is directly charged by the converter and the BCC relay manages whether the chassis (engine start) battery is also charged. Since you say the start battery is getting charge voltage, that part must be working. However, 13.07v is a bit low - I would have expected the 13.3v-14.3v range.
If the house Aux battery is not receiving a charge, I can only guess it is not wired in properly. Start with verifying its battery plus cable (from the converter) and the negative ground cable.
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Gary Brinck
Former owner of 2004 American Tradition and several other RVs
Home is now West Palm Beach, FL
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