Sounds like you just ran out of batteries...
You will have to learn what is needed for the different modes of using things...
Not knowing what batteries you have or what all is running it is hard to say what has happened but it really sounds like you just started running your battery down as you went down the road.
If you was using a POWER INVERTER running from your battery to make 120VAC while enroute will not last very long depending on how many batteries you have in the bank. Most basic things all run on 12VDC so they can run anything you need them getting their power from the battery source. The 120VAC items either need to be hooked to a shore power connection, AC generator, or Power Inverter that runs from your battery. If you were indeed only using a power inverter and only have a single battery you will not get a very long run time as the Power Inverters that are large enough to run 120VAC for many high wattage things will really need many batteries to make them work very long...
I am thinking you may be using the term INVERTER for your CONVERTER/Charger unit. The CONVERTER/Charger unit has to be feed with shore power or an AC Generator to produce 12VDC to charge your battery...
Th eonly way the battery may be charged while enroute is a trickle charge from your truck start battery system and if you have a bunch of 12VDC items on while enroute you can very easily run the battery down. You can only expect around 6AMPS or so of trickle charge coming from the truck start battery system.
Hopefully you haven't hurt your battery yet by discharging it below 50% charge state which is only 12.0VDC and can get it re-charged again and then learn how your new trailer works power source wise.
Just my thoughts with what information I can use from your short statement...
Roy Ken