After driving for a few hours when attempting to accelerate, the engine starts running rough?

Yep, I have seen a weak fuel pump cause this problem, we should run the codes though, this guide can help:

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

If no codes are present, we can do a fuel pump pressure test, you can rent a fuel pressure gauge from the auto parts store for free or cheap.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Key On Engine Off 35 - 45 PSI
Key On Engine Running 30 - 40 PSI

Here is how to change the pump out in case you need it. Check out the images (below). Please let us know what happens.

I have two codes showing P0420 and P0401. I’m thinking with as old as the car is the catalytic converter is probably not in the best shape, but what frustrates me is my car does not act up until I’ve driven it for a few hours. I do a lot of stopping and going on the mail route and it seems to run perfectly fine for the first couple hours then all of a sudden I’ll take off from a stop and get somewhere between 30-50 MPH and it feels like it gets stuck so I'll try to push the pedal to the floor and it won’t go.. So, I pulled over for 10 minutes and shut it off then it worked fine for a while. sorry for the long posts but would the catalytic converter wait that long to show symptoms? I plan on having my mechanic replace my EGR valve just wondering if I'm heading in the right direction. thanks for your help.

The diagnostic trouble codes (DTCs) P0420 and P0401 relate to different issues in your vehicle. Here's what each code typically indicates and some possible causes and solutions:

P0420: Description: Catalyst System Efficiency Below Threshold (Bank 1)

P0401: Description: Exhaust Gas Recirculation (EGR) Flow Insufficient Detected

So, I would say the EGR valve is sticking open, or the catalytic converter needs to be replaced.