Engine is running rough

Check the TPS sensor. If the ECM cannot track it properly it can cause rough running and it would throw other things out as well. STOP disconnecting the battery as well. That resets the idle learn, trans and more.

replaced tps sensor and its not better. its dying when I slow down or come to a stop. it doesn't want to take the gas. and its back firing.

I would start by doing a compression test to see if we have an engine or not. When the engine misfires it creates lean codes. Can you follow this guide and get back to us?

https://www.2carpros.com/articles/how-to-test-engine-compression

and

https://www.2carpros.com/articles/symptoms-of-low-compression

and

https://www.2carpros.com/articles/the-reasons-for-low-compression

Cheers, Ken

Dying when slowing or idling is a symptom of a dirty idle air control and losing it's idle control.

If the compression was bad wouldn't it run bad constantly?

Yes it would, can you shoot a quick video of how it is running so we can see? Upload it here from your phone.

Anything on this problem?

My husband did a vacuum test and he came to the conclusion its a clogged converter. He said there's no way to get it off. The way the tbird is made you can't hardly get to anything. Any suggestions?

Those are a tough on but it can be replaced, Here is a guide that will give you an idea of what to do to fix the problem.

https://www.2carpros.com/articles/catalytic-converter-replacement

You will need to raise the car up safely,

https://www.2carpros.com/articles/jack-up-and-lift-your-car-safely

Here is what it will be like for your car (below)

Please let us know what happens.

Cheers, Ken