2002 Cavalier having trouble shifting/accelerating...with AC on?

I have a 2002, automatic Chevy Cavalier that has roughly 98,000 miles on it. Since the
weather has been heating up I've had to turn my AC on but I've noticed a change in my
accelerating and shifting when my AC is on. I honestly don't know if they could even
be remotely related but I've tested this multiple times. I'll turn my AC off and my
acceleration is normal...(this car has always had weird acceleration/shifting problems.)
When the AC is on however it shifts hard! Also, if I watch the tachometer I can visibly
see it struggling. It will stutter and once it does shift the car jerks enough you can feel
it. The speedometer will also make a jump and then quickly go back down...a few
weeks ago it was shifting really hard and stuttering really bad. I took it into a mechanic
and they had it for two days before I finally got it back and it was just gone. They were
trying to do a diagnostic on it but said my car wasn't having it and there were misfires
in the engine until they took it out on another test drive and it was shifting normally.
Can the AC have an impact on the acceleration/shifting? If so, what is possibly
causing it and how do I fix it? I'm a young girl with very little knowledge about cars and
very little money to put into my car so any tips, tricks, or just good advice will help!