Assuming that your unit is manufactured by Dometic, and is relatively new, 4000 W should be plenty of power to run one 15,000 btu AC unit. At least that is what Dometic says:
https://www.dometic.com/b97fb7b3-584...758792f7.fodoc
I little investigation might help us narrow down your problem. What happens when you go to Med. or High speeds when running the generators? Do you trip a breaker? Is the breaker on one or more of the generators or is it in the trailer? Does anything else happen?
Other thoughts:
Are you able to get up to Med. and High speeds when connected to shore power?
Are the eco-throttle switches on or off during your testing?
Are you confident that your cord isn't damaged, and that any "dongles/dogbones/adapters" that you might have connected to it aren't showing signs of overheating?