I have a 1996 Isuzu Oasis minivan (same as Honda Odessey). It actually has a Honda 4 cylinder engine that I had installed a year ago that has about 50k miles on it. The car hesitates when the AC is turned on as it will die down and sometimes it does die at a stop light. The mechanic who put the engine in it can’t seem to find the reason.
The only real importance of the AC is that running the compressor puts an extra load on the engine. The engine is apparently borderline in terms of running well and the AC is tipping it toward running poorly. This is worse with 4 cylinder engines, and especially so in vans since they have enough trouble just pulling their own weight, let alone that of the whole van + passengers + cargo + running an AC compressor.
The place to start is with the basics. Clean air and fuel filters. Good spark plugs and wires. Check the fuel pressure. That mechanic has to have done something with it besides stare and shrug (though that is what some do). Report.
Clean the AIS motor. If it’s dirty it will not freely adjust the idle in a timely manner.