Other than having your amps and volts a bit confused, the answer to your question is yes,.....inverters hate low voltage and must be close to the battery. So, get your house battery(s) installed, and make sure they are getting 13+ volts when engine is running, and you will likely not have any more problems w/ the inverter. If you do, the wiring between the inverter and the batteries is probably too small.
Rich
'01 31' Rexall Vision, Generac 5.5k, 1000 watt Honda, PD 9245 conv, 300 watts Solar, 150 watt inv, 2 Cos 6v batts, ammeters, led voltmeters all over the place, KD/sat, 2 Oly Cat heaters w/ ox, and towing a 2012 Liberty, Lowe bass boat, or a Kawi Mule.