If your authorised representative in the EU put your products under his/her own name, then she/he takes over your responsibilities. In this case he/she must have sufficient information on the design and production of the product, as he/she will be assuming the legal responsibility when affixing the CE marking.
Many of the larger inverters come with a built in charger. Typically a 2000 Watt or larger inverter will have a 50 to 100 Amp 3 stage charger. These are much better than the typical RV converter/charger. If you are planning on a more powerful charger anyway, the combo units make sense.
Factors such as battery size, converter output rating, amps and battery discharge level determine the power requirement for an RV battery. For example, a 100A battery charger with a battery bank size of 600 and an 80 percent discharge level requires approximately 1.8 hours of power to fully charge. That number increases drastically if the discharge level drops to 20 percent, in which case the battery requirement is approximately 7.8 hours.