Hesitates and skips going into gear btwn 50 and 60 mph

How many miles on this engine? If there is an engine misfire, the trouble code should tell you which cylinder other than p0300. Then on a particular cylinder, you check fuel--spark--compression. Any applicable trouble codes? Did you use a gage and check proper fuel pressure?
A problem at higher rpms, the generic info says to check for a blockage of some kind, fuel--air--exhaust.
A problem at idle, generic info says to check for a leak of some kind, fuel--egr--vacuum.
When you say takes a minute to change? Are you talking about shifting gears--automatic, if so check vehicle speed sensor.

At a steady 65 mph, the torque converter clutch (TCC) is engaged. When you accelerate, the ECU disengages the TCC to gain extra torque for acceleration and then re-engages TCC when speed is steady. Its kind of like having an extra gear.

check the cap and rotor button and the plug conection at the distribtor from the main wiring harness could have water in the conection

What has been tested ,since you know what codes you have

Did you check the fuel pressure before and after replacing the pump ?
Is the check engine light on ?

i had this similar problem on my kia optima. Does it hesitate when it switches gears when accelerating if so. The problem is the fuel pump. i had to replace mine and that solved my problem.

Change the fuel filter & make sure the fuel pump is putting out enough pressure. Good luck!

SOUNDS LIKE A TRANSMISSION VACUM MODULATOR,THET ARE CHEAP,MAKE SURE VACUM LINE DOESN'T HAVE ANY HOLES OR DRYROTTED AND YOU HAVE VACUM

You have a hesitation. A hesitation is cause be either:
1. bad spark plug
2. bad spark plug wire
3. bad or leaky or plugged injector
4. timing is off
5. leaky vacuum hose

simple tune up could do it, or a bad MAF or MAP sensor could give similar problems