This is all you need. Should be fairly straightforward to do using an Arduino or similar, a relay, and a few misc parts.
You would want to actually interrupt the 24v signal to the AC
while the car is charging and then monitor that line to determine
if a call for air is initiated from the thermostat. This allows
you to disable the EVSE, wait a second, and then start the AC so
there is no chance of both running at the same time and is a way
to avoiding all the inrush current issues and fast switching Adam
mentioned. The simple relay method you suggested may not drop the
EVSE load fast enough before the AC starts, that all depends on
your particular compressor and EV, etc. Anyway, if you so
determined a few seconds after the AC starts you could then
restart the car charging at a lower current, etc. There should be
no internal rewiring of the EVSE or the AC required.
You would definitely need some electronics experience and design skills to do this but it's also very possible. If I was stuck and couldn't get a line from the panel to a charging location I might look at doing something like this but I also doubt a little bit that it would be as hard to run a circuit as you think. I replaced my main electrical panel and needed to run a new grounding/bonding wire clear from one side of the house to another, including through some finished spaces, and was able to do it. So in the end I do agree with Adam's conclusion that it's probably faster and easier to run a new circuit. I just wanted to point out your solution is a bit more feasible than he had indicated.
-Ben
I recently moved to a new house and the electrical panel is on the opposite side of the house from the garage. It would be very difficult to run a new circuit to install my Openevse charger. However, the Air conditioning compressor is on the back wall of the garage, which is an ideal spot for the charger. It is a 50A circuit so it would be substantial enough to charge my Fiat 500e at 6.6kw but not while the AC is running. I could just make sure the AC is off while I'm charging the car but I would like to figure out a more sophisticated way to do it. I have thought of two possible ways to make this happen but I'm hoping that someone might have an even better suggestion. My first thought was to put a 24v relay in line on the pilot pin. When the air conditioning thermostat sends 24v to the compressor it would energize the relay and disconnect the pilot pin, dropping the pilot pin voltage to zero and stopping the charge. My other thought was to send Rapi commands to the charger via wifi. The advantage to this would be that if there is enough overhead on the circuit I could issue a command to reduce the charging rate rather than stop it all together. I haven't figured out how exactly to do this but I was thinking an electronic imp could do the job.