Definitely the generator, through the convertor. It is more sensitive to the coach battery system, has larger wiring to the coach system, and costs a helluva lot less than running the V-10.
The alternator will "see" the chassis battery first since it's the closest (wiring-wise) to it, and when the chassis battery is satisfied, will reduce output to maintain it.
2005 Georgetown 342DS XL, Full Banks Package
2005 Liberty Renegade 4X Toad
1989 Wrangler Sahara Toad
1984 19.5' Beachcraft i/o 5.o liter, 4-bbl (and you thought your Moho sucked gas!)
D/W Carole and Maggie the Teacup Lab (Black Chihuahua)