Rough idle that gets worse with A/C on, rough acceleration, misfire?

Hello, the check engine has been on then there is a trouble code stored in the engine computer. Your local auto parts store will scan the engine computer for free, just write down the code number and don't let them sell you any parts yet until we figure out what is going on with the vehicle.
The reason the condition gets worse with the A/C on is the A/C compressor puts a large load on the engine, and with it not running correctly the lack of power is much more noticeable. The codes that will be stored will have a letter on front of them top, for example P0300 is a powertrain random misfire code. The letter is important because it tells which system is setting the code.
What you are describing sounds like a possible Catalytic converter failure, which happens when too much unburned fuel exits into the exhaust (a rich mixture). But see what code(s) are stored first and we will go from there.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Well, knowing what code is stored in the engine computer (ECM) would give us some direction as what might be happening, if you have multiple cylinders misfiring that will feel like a lack of power, it was the "slow at acceleration" part that sounds like a restricted exhaust type of symptom. But have the ECM scanned for codes and we will go from there. That way if you are having just cylinder misfire codes, I can walk you through some easy tests to see what might be causing the misfires per cylinder. Do you have any testing tools, such as a 12v test light or multimeter? If not grab an incandescent 12volt automotive test light while you're at the auto parts store, they will scan the vehicle for free, they do that because they want to sell parts, but just write down the codes and then I can let you know what needs to be checked.