It makes very little sense to get a 3000 watt inverter if you'll only have two batteries. It's somewhat akin to attempting to tow a massive 5th wheel with a F-150.
If you want to energize the whole electrical system with the inverter, you need some sort of a transfer switching arrangement that will not allow it to be possible to connect it simultaneously with the shore power or with the generator power. (In saying earlier you could use the existing transfer switch I assumed you did not already have a generator connected to it. That was a bad assumption. It's not possible to connect three sources to the two inputs of a single two-way transfer switch.) A parallel connection with manual disconnects is not a safe or appropriate option; anything that relies only on one's memory, rather than some sort of physical interlock, to prevent connecting two sources simultaneously is unacceptable and contrary to electrical codes.
Perhaps the simplest/lowest const way is to connect the inverter output to a socket you can plug the shore power cord into. If the power cord is permanently attached to the RV, you might be able to put this socket in the compartment where it's stored and simply plug it in whenever you stow the cord when breaking camp.
An automatic (or manual) transfer switch also works fine. It's obviously more costly than a simple socket, but may be more convenient. The transfer switch will generally have to switch both the hot and the neutral lines, both hot lines and the neutral if you have a 50A RV. You typically cannot use a transfer switch intended for a residential emergency generator that only switches the hot lines.
