The frig....would that be too much 'pull'?
Yes, between the fridge and the coffee maker, that would exceed your 2,000 Watt Inverter's capacity.
I think the real issue is that your batteries are not fully charged when you are trying to run the coffee maker. Presumably, you are trying to make coffee in the morning, after you have camped all night. This means that your batteries have been running your lights and refrigerator overnight and they simply do not have enough energy left in them to power your Inverter for a full 2,000 Watts.
If you want to test this, one morning, at a campground where you have access to shore power, and after you have been plugged in for more than 8 hours, disconnect your shore power and ensure your fridge is turned off, and try to run the coffee maker. If you get coffee, then your batteries were at a low State of Charge (SOC) when you tried to make coffee in the past.
The good news is: that if the above test gives you coffee, you can fix your issue by installing an adequately sized Lithium battery bank.
What is an "adequately sized battery bank" you ask????
Well, the answer is different for every family, and is based on how much energy your family uses each day, the weather, and how many days you want to camp without being plugged into shore power (aka: Boondocking).
When you read the above linked thread, you will get some idea of what is involved in figuring out your battery bank size.
PS: you can use the "Reply With Quote" button at the bottom of the post you are replying to, as I have done here, to let people know what post you are referencing when you are replying to someone.
