For your house the M116A2 with the propper Gen Set (forget about the 3 kW sets with two small engines, the somewhat 15 kW set) is big enough with regard to power output. And you can safely pull that trailer with its overrun brake device (inertia brakes) ith yout truck.
Anything larger will theoretically kill you, as said in the obove statements. This not neccessarily means, it will do so, but the risk is to high. And I do not know the legal requiremnets for your inshurance.
However, for a 2 1/2 ton trailer without brake connection (air, electric or override), I would not drive more than in the close neigtborhoud, exept I use a at last 5 ton heavy agricultural tractor. But from LA to your place it is a little to big distance for an AG tractor. Or at least a Deuce. This is not the problem of the pulling power, it is the braking issue!
And if you connect the Generator to your house, do not forget to diconnect the harness to the supplier net or you feed them all. There are relais on the market available to do that for you automatically, at least in Europe.
Wolf