the RV already has an onboard battery charger built into its electrical circuits... you should find it in behind the power distribution panel (get to it from behind a panel in the basement?).....
you could call the manufacture with the serial number and see what they installed, but as NO ONE knows if a previous owner has changed any thing.....
you seem to be aware that a lifpo4 battery charges at a different algorithm than flooded/gel batteries do, so you will need someone to either reprogram the charger you have (if its re-programmable), or replace it with one that has the correct algorithm in it....
as for the title of your post, an INVERTER is an "add-on" device that can be used when you have a big battery bank, or solar, or both.... (2) 100amp lifpo4 batteries is a reasonable size, and the minimum capacity that should be used with a 3000w inverter...... which, the inverter then "inverts" the 12volt DC power into 120volt AC power, so that you can watch tv, or run the microwave, vacuum cleaner, ect... without being plugged in to a power post or running the generator..... or, in hot weather, you could run the air conditioner, but I would recommend if you want to run the AC without being plugged in, you need about twice the battery capacity, AND solar panels.... because if you dont have a power post to plug into, and you run the AC til the batteries are dead, you are all out of power until you find a way to replenish them...