"I'm trying to figure out the best way to wire in a battery to the
trailer.It has a 12v to 110v ac converter and it "looks" like that
gets fed from the tow vehicle"
I doubt that it's wired that way, All TT I've owned have the battery wiring already installed. Usually the battery at the front in the A frame. You should 2 heavy duty cables (ground and +ve); The +ve should go all the way back to the 120/12 converter/inverter.
"if anything to have 2 batteries hooked to tow vehicle ,one in it, and one on trailer."
Not sure why you want to do this - if you need to charge the TT batteries, there is a pin in the 7-pin connector which is used for this purpose.
"I'll also want to add a low voltage cut off";
Again, not sure why you want to do this; I have digital voltmeter attached to the dual batteries and just keep an eye on the voltage; I have a battery cut-off which disconnects the battery from everything. I have a solar wired in, so my batteries never go belo2 12.7V.