1999 Jeep Cherokee hesitates after start and ac stops blowing after hour driving

My jeep is having two issues. First, almost every time I start the vehicle it idles fine, but then when I start to accelerate it bogs down for 1 to 2 seconds. I will accelerate through it and after that it runs fine and doesn’t do it again until the next time I start the vehicle. My second issue is that after driving for a couple of hours with the AC on, the flow of air out of the vents drops. The air is still cold to the touch just barely blowing. Once I cut the motor off for about 30 minutes it works fine again for a couple more hours. Also, when the intensity of the air coming out of the vents dies down the blower motor sounds like it is working harder to put out the little bit of air pressure.

I forgot to say that this is a 1999 Jeep Cherokee 4.0L I6 with 214,000 miles.

Is it coming out the defrost vents? It still uses vacuum operated doors and the actuator could be leaking down or you have a vacuum leak. Have the plugs been changed? Since it’s the first start I would suggest a leaky injector or low fuel pressure.

Next time it happens I will check to see if it is coming out of the defrost vent. How would I repair a vacuum leak? Also, I wonder if it is difficult to check, and reinstall a new injector?