Why won't my 2006 Ford Fusion accelerate while the a/c is on?

My car has 198,000 miles. We had to replace the engine a couple years ago, the replacement engine had 68,000 miles when we put it in. In the past 4 months it has become a nightmare to drive. It WILL NOT accelerate while the a/c is on. What can I do about this? It's driving me insane, Texas heat and a car that I can't drive with the air on sucks!

Does that have a WOT cutout relay? Substitute another relay to eliminate that possibility?
I think the ac system can be diagnosed with self test codes,
as well as the engine management system.
A compressor that drags can also be at fault. I'm not aware of a
known problem. You could try a cold short road test with no belt.
Perhaps something had to change during the engine work?
Your ford dealer can tell you if this has been happening
enough to generate service bulletins.
Look into what climate control modes makes the compressor run.
Then look into what setting(s) you experience the power loss.
What's different, and when. Then formulate your tests for a diagnosis.

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