When the back A/C starts, the genny dies!

The caps are a good place to start, but have you done any battery bank changes lately?

When I went from a single G24 to a pair of 220AH batteries my 2K genny would no longer stark my 9K BTU a/c with the converter on whereas before it would them both without issue.

So if you have upgraded the charger and/or batteries it could be drawing more than you think. If not I would start with the caps.

Or your fuel filter is clogged. Have you serviced it? QD is an inverter type genset. It steps up the RPM when the load increases and if the ff is clogged, it dies from lack of fuel. Shuts off as it can't regulate the load.

Also - I have read that as air conditioners age they draw more amps especially during startup - sometimes a hard start capacitor will solve this issue.

x2 on the caps. Sounds like a faulty start cap.

Some info. here. RV AC capacitors As mentioned, if you are going to take a cap. out, short it out first to discharge it. If you can't test a cap., I would just go and replace one first and see if that fixes it. If not, re-install it in the other AC. Or spend the extra $20 or so and just replace it in both AC units. I guess it's also possible to be a faulty start relay but more likely a cap.

You won't be able to measure the actual startup current with a multi-meter. It actually goes as high as around 6 times the run current for a small fraction of a second and it won't show on your meter. You can find the starting current in a AC manufacturers tech. data.

Some info. and pricing on Coleman caps.: Coleman AC parts Maybe you have another make though.

Mine did that and it turned out to be the start capacitor on the roof air. Go to youtube and watch a few videos on testing and replacing both the start capacitor and the run capacitor.

Since the generator checked out there may be a issue with one of the AC's pulling more than it should. Have you tried starting the rear AC first? Maybe it's pulling more at start up than it use too.
Also have you tried to push the generator in different ways? Try one AC plus the microwave and a hair dryer, enough to come close to full load.