Okay, there are a few things wrong here.
There are 2 different kinds of vacuum,
1. Ported vacuum ,which sucks more when you open the throttle. This is the vacuum that the distributor should be hooked up to. At idle, there is no ported vacuum.
2. Manifold vacuum. This is the vacuum that runs most of the vacuum accessories on a car. This one sucks most at idle, and decreases as you open the throttle.
From your description, it sounds as if the distributor is receiving manifold vacuum only, which is incorrect. This has allowed the vacuum to be way too advanced at idle, but it retards as you step on the gas, which is the opposite of what you want. To make matters worse, it seems as if the initial ignition timing has been retarded to compensate.
You need to make sure the distributor receives ported vacuum AND then you need to readjust the ignition timing at idle to run properly.
Now this is where it gets complicated. Many older carbureted cars have a vacuum switch on the intake manifold. 2 vacuum lines run to this switch (one ported, one manifold vacuum) Then a single vacuum line runs from this switch to the distributor.
The switch is supposed to send manifold vacuum to the distributor when the engine is cold (less than 120 deg. F) and switch to ported vacuum when warm.
Over time, these switches seize up so the engine gets manifold vacuum all the time.
I would suggest bypass this swithc all together and run a vacuum line directly from the ported vacuum source on the carburetor directly to the distributor. It's the only vacuum source on the carb that is above the throttle blades, but you may need a vacuum gauge to make sure you have found the right source.
Your car will run much better. Be sure to cap any manifold vacuum source you are no longer using.
Finally, your engine shoudl not die when you unplug the vacuum line. I suspect someone set up the ignition timing with the manifold vacuum line installed. This has completely thrown off the timing and it is too retarded for most of the car's operation. so, after you get the proper vacuum line installed, temporarily disconnect and cap the line and reset the initial timing with a timing light to factory spec.
You will probably find it needs to be advanced a lot, but your T/A will then run like a scalded cat!!