So it was my first time replacing a lock cylinder. I purchased a new Autocraft lockplate tool (I guess you get what you pay for with that Advance Auto piece of ****). A few turns and the nut broke off! Now I can't get the lockplate tool off my car? Any Ideas? Could AAA remove it?

Here is a picture of the current state:

 

How much did you reef on it? Nothing about using that tool needs to be that tight. Not trying to be a harsh or anything, but you know how to use that tool, yes?

Getting it off the column:

Hold the sturrup and unscrew the nut that's sitting on top of it. That will release the lock plate. Then use pliers to unscrew the tool off the steering shaft. Throw tool in garbage.

You might need another identical tool if you still need to re-install the lock plate after you get the FUBAR'ed tool off.

 

The nut you should be turning to depress the lockplate to remove the circular
clip holding it on is the one still there. Turn to the right until it's far enough down to remove the clip and then unscrew it to remove the tool
If you were turning a nut that used to be on the end of that thru-bolt the nut that's still there is what kept the bolt from being able to turn hence breaking the nut off

 

I watched a YouTube video and the video said tighten it and the Lock Plate tool pushes the lock plate back on the spring until the snap ring gets lose and you move the snap ring forward then you loosen the Locke Plate tool.

I kept turning the lock plate tool and it seemed like the lock plate never mode back and the snap ring never loosened!

With a few turns the lock plate tool broke.

I finally got it off with a pair of vice grips. It seems like was made of cheap pot metal.

 

That's the thing, I was never able to turn it far enough to wear the lockplate moved back and the snap ring could get lose. It broke before I could do that!

I finally got it off using vice grips.

It seems like the thru bolt on the lock plate tool is made of cheap pot metal.

 

The snap ring doesn't just come loose. When you get the lock plate down far enough you need to pry the ring out with a pick or tiny screwdriver and slide it on to the barrel where you can leave it until you need to slide it back in or just simply remove.
And the nut on the end that broke off was just to hold the bolt in place while you tighten the lower nut to depress the lockplate

 

I brought snap ring pliers to pull out the snap ring but the thing is the lockplate never moved. I couldn't get it to the point where it moved down far enough to even pry behind the snap ring.

The tool broke with only a few turns.

Every video I watched used a ratchet or a nut driver on the end nut of the thru bolt. So I thought that's what you are suppose to do.

 

It's also not an actual snap ring either. Snap rings have tiny circles on the ends for the points on the snap ring pliers to fit in. This here is just a plain ring held in place by a tiny bit of tension from spreading the ring to get it in it's groove. Then the lockplate holds it down.
When you get another tool, put it together the same way, BUT then just put a wrench or socket on the top bolt to hold it in place while you tighten the bottom nut at the same time. It will force the plate down and give you the space you need