This sounds like what was happening on my car when my cooling problem started. When the battery hits a certain temp it will dedicate the entire cooling capacity of the AC compressor to the chiller block for the battery coolant loop.
My battery could get so hot the car would force a stop (stop now safely) and that still wouldn't generate a code. The easiest way to confirm will be monitoring the coolant temp through an OBD scanner.
I have an OBDLink MX+ (Bluetooth, supports high speed and medium speed CANBus scanning) that I use with FORScan Lite on Android. You can monitor the chiller solenoid that directs refrigerant to the battery chiller, coolant temp, coolant pump speed, coolant diverter position and compressor status. I lucked out and got a ScanGauge display configured for Focus Electric, so I can keep track continuously.
When the battery temp reaches 97F, it will start chilling coolant going into the battery loop. In my case the temp would not go down once that started - in fact the load from the compressor would actually make it hotter if it was trying to cool while charging.
I'm not sure the exact temp, but when the system pulls out all the stops to try and cool the battery it will no longer cool the cabin. If it's not blowing cold and the compressor is still running, that's likely what you're dealing with. You will also want to make sure your refrigerant is not low, it can cause other problems where refrigeration won't cycle properly - and the car will throw no codes for that either.
Your motor will generate heat, your charger will generate heat while charging, your DC to DC converter will generate heat turning HVDC to 12V. If cooling is working properly, your battery should be able to stay below 100F in all but the worst conditions - but Ford CANNOT tell you what amount of heat the chiller should be able to move out. They blew it off as being a result of charging in the sun until I proved I could reproduce it on demand.
Hope it works out better for you than it has for me, though you might luck out and find that it's just a pump and filter problem. The impellers can break and end up in the filter, which can prevent coolant flow through the battery. I also wouldn't rule out the evaporator coils icing over, but that depends on how long you let it sit before trying again.
2012 Candy Blue FFE
33.5kWh battery pack
CHAdeMO DC Fast Charging