Transmission pulls but when slowing down or stopping then gasing it, the transmission slips and the catches and jerks the car.

When you say it "jerks," this description could fit several actual symptoms. If by "jerks" you mean the engine misfires, it could be caused by the need for a major tune-up (including plug wires and distributor cap), or it could be a problem with fuel delivery, contaminated fuel, or defective components in the fuel system.
I assume the CHECK ENGINE light is on (and has probably been illuminated for some time now). Begin by doing a readout of the stored codes, and use the results to begin your diagnosis.
If by "jerks" you mean the transmission is slipping (engine revs but car slows down or doesn't accelerate), you have a transmission issue. If the transmission fluid and strainer/filter have not been replaced within the past 5 years or 50,000 miles, have a complete transmission service performed.
If by "jerks" you mean that the steering wheel wobbles or pulls, you have a problem with the front suspension.
If by "jerks" you mean that the car shudders or pulls when you apply the brakes, you need brake work.
I think I covered all of the "jerks." ;)

CK TRANSMISSION FLUID

Hi there,

This is a classic condition of a 'slipping' transmission.

The problem could be anything from bad fluid, poor fluid pressure, faulty pressure valves, faulty solenoids, loose bands or even internal mechanical failure.

First step would be to flush your transmission and refill with new fluid and replace the transmission's internal oil filter.

If problem persists, then a transmission overhaul or 2nd hand replacement could be in order.

Transmission is due for a rebuild

Stop using it --- as it will only overheat more
& ruin hard parts inside it

There is no fix for slipping

This sounds like your transmission is slipping. When it slips you will lose power when it catches back that's when you get the ****. Hope this helps.

You may need a transmission flush, if one of the valves sticks in the transmission it may not make a quick decision to shift when in between gears. Worst case ...this may be a precursor to worse problems, like a transmission rebuild.

It seems as though the Transmission clutches are slipping if it's an automatic or the clutch is worn if it's a standard. If it's an automatic transmission check the Transmission oil it should be clean and no burnt smell. You will easily recognize burnt oil by it's nasty smell.

You could have a slipping clutch if it's a manual transmission.

Agreed. I had the same problem, transmission would lag between 1st and 2nd, and it would **** violently sometimes from a stop. Anyway, they had to rebuild the transmission. I'm not sure how much it would be as I only paid deductible from warranty ($100.00) but they kept saying average rebuild price on 2003 impala is about $1,200-$1,500.

Fill the transmission up to full with atf fluid. Check while running.