A little confused here.. which is perfectly normal for me..
1- Running your 2000 watt generator plugged into your shore power (Correct?)
2- Running your 1600 watt inverter while your shore power is plugged into your generator, at the same time? (Correct?)
How is your inverter's 120VAC output wired?
So you are pumping 120VAC from your generator and 120VAC from your inverter into the TT's 120VAC system at the same time?
I hope not!
What you may want to do is:
1- Wire your 120VAC that feeds your TT's charge controller into its own AC breaker. (I did this for my solar connection)
2- When you want to run your microwave,
..... Turn off the TT's charge controller breaker which will eliminate the current needed to charge your batteries, and will allow your generator's output to go to the microwave and not split its out put between the microwave and the TT's charge controller.
..... Turn off your Inverter (should only be used when NO shore power or generator is connected)
3- Start your generator and you should find that it will easily run your microwave (make sure your not running your coffee pot, hair dryer, AC at the same time)
4- After the microwave (hair dryer, coffeepot..) is done, turn the AC breaker back on.
MOST inverters are NOT designed to be run at the same time your shore power is active. If they happen to get out of phase you can have some very interesting events happen. Automated systems turn on/off the inverter based on shore power availability.
Just my thoughts,
2013 Jayco Eagle 284BHS
250Watt Grape Solar Panel, MorningStar MPPT 60 Charge Controller
1500 Watt Ramsond PSI, 2 Trojan T145 Batteries (260Ah)
2 - AirSight Wireless IP Cameras (used as rear view cameras)
EnGenius WI-FI extender, D-Link wireless (n) modem
MagicJack Internet Phone
2012 Ford F150XLT, EcoBoost w/3.73
157" Wheel base, HD Towing Package
Our Solar Album http://www.jaycoowners.com/album.php?albumid=329