I can guess your AC does not have fan switch to force it to low speed?
We spend lot of days in our campers with 124F outside, cooling down to 100 after midnight.
We got used to AC running whole night, but forced to low speed.
Beware that even AC is cooling center of TC to comfortable temperatures, the cabinets on south side can reach 140F, so don't keep perishables in them.
Ours sons were being relatively quiet babies, bit I still remember that between 1 and 2 years old is the hardest part as they get mobile and want to explore everything, while showing very little common sense and self-preservation. Can only imagine what it is with twins.
I think next summer this is going to be completely different story.
But I admire your drive to try. Most of people would spend those days in comfort of their sofa and TV remote.
We have a thread about RecPro AC.
I put 1 of them on my Sprinter conversion and it seems like very nice unit, although I did not take it for overnight in 120 yet.
100F in dry climate is not bad. I am on East Coast right now and with only 90F I am wet stepping out for just seconds.