Briefly; your RV uses 2 different types of "power" or electricity (I sometimes use them interchangeably) - 120vac from the electrical shore connection and 12vdc which originates with your battery(s). Two complete separate systems that operate independently of each other with the exception of the CONverter (changes 120vac from shore power to 12vdc) that uses the 120vac (shore power) feed to then convert and charge your batteries. The converter can also run your 12vdc functions in a limited fashion if the batteries were bad...but it can ruin it.
Your air conditioning, electrical outlets, electric fireplace, microwave, ceiling fan (if equipped) all run on A/C shore power. Your furnace, lights, leveling jacks along control circuits for thermostat relays, furnace, etc. run off 12vdc so in that sense they are interdependent.
You mention converting from 50A to 30A at your brother in law's; realize there is a huge difference between 50A vs 30A. Without going into detail the 50A can pull over 3 times the power that a 30A can. Sounds like the BIL has a 30A connection which a 50A trailer can trip without a problem. In the case of the BIL it could have been from trying to use too much power.
Also, your EMS (PTX-50) will have some sort of delay when coming back on after cutting power to the trailer for some anomaly...maybe that is something you've experienced.
Lots of bits and pieces in the electrical system of an RV. Knowing how it works, what works what, what they operate on and how they affect each other is essential in having a trouble free camping experience. As well, owning a (or many) VOMs (multimeter) and know how to use it is, IMO, a necessity. They will literally let you "see" electricity and various electrical attributes vs guessing.
I can find nothing that indicates you have an inverter. At the time your trailer was built they would typically be installed on an RV with a residential fridge but I can't find that it has one.