Here's a link from someone with a similar basement AC condition, but they never posted the solution. You might revive it so others who subscribed to this thread will get notified and maybe that will solicit a good answer and fix? TBD.
* Always make sure you have tight connections!!!! My guess is that you are looking for a loose neutral wire lug. I.e., with both compressors running at 24A -28A a loose neutral return wire may cause the compressor to overheat and shut down, but not trip a circuit breaker.
* Always make sure your capacitors are in spec.
Note: If you your multi-meter does not read capacitance you can google search how to measure capacitance using a formula.
Note: Some people say they were able to revive their weak compressor by installing a Supco SPP6 or SPP4E Hard Start Kit in place of the OEM Hard Start Kit. See my other thread on this subject.
Since you have 50A service, where did you switch L1 & L2? Was it going into the ATS?
What type of ATS do you have?
What year and model RV do you have?
Do you know the model of your Coleman Mach?
Does your AC work properly on generator power?
What type of generator do you have?
Do you have a 30A "Dog Bone Connector" to convert your 50A (L1 + L2) into a dual 30A service?
From the factory that would but L1 (red wire typically) on both legs. However if you switched legs then you would get the shore power L2-black-wire on both legs to the RV.
Using the Dog Bone may have a positive affect on the ATS relays. (Maybe, I'm not sure. But it is worth trying since it is so easy to test.) And both compressors should work on 30A service.
I'm going to guess you have a Parallax ATS-5070 (like me). So look closely at the wire diagram below and you will see there is only 1 "Neutral Relay" and 1 "Hot Relay" in your ATS.
However, these are 8-pin relays and my guess is that you have a burnt point problem... or the generator Neutral wires feeding the ATS are a problem.
* You might first try banging on the relay box with a hammer.
* You if your AC does not run right on generator power, then you might try disconnecting the ATS-generator wires and see what happens.
BASEMENT AC #2 RELAY WORK AROUND
If your #1 compressor circuit is working, but your #2 compressor circuit is suspect, then you might try this:
* Swap the basement AC #2 relay pins 6 & 8 and put these wires on 2 & 4. These pins are are normally not used, but will function just like 6 & 8... so you will be using effectively "new" points on pins 2 & 4.
It's a long shot, but when you don't have new parts in the field it may be your last hope to get both compressors running at the same time.
Note: I don't know if you can start compressor #2 without having first started compressor #1. This might have something to do with a reversing valve in the system. However, I have never tested this. Maybe someone else can tell you if you can start compressor #2 first?