You have 3 batteries yes? Two 27s on the trailer and something in the truck.
The microwave is 1050w input power or cooking power? Input power it will draw 90+ amps, cooking power it will draw closer to 120+ amps. If using a modified sine wave inverter the power will be reduced by 20% to 50% and cooking times will be longer.
The long #6 will supply 20 to 50 amps with the balance coming from the two 27s. The truck battery probably will not discharge as the alternator should hold voltage above 13 volts at the front of the truck.
For maximum transfer consider some shorter jump cables direct from the truck battery to the trailer pair. Look for #4 copper cables.
Best to have 4x group 27 on the trailer to drive a microwave.