I made a discovery on my problem, I noticed I have misfires on 1 or more cylinders when my sputtering happens. It is totally random which cylinder. I've seen one spot when all 6 misfired simultaneously. Now to figure out why I'm getting random misfires...

I also believe I have a bad motor mount. A friend had me put her in drove, step on the break and run it up to about 1500 RPM'* and he said the motor looks like it wants to jump out the hood. Now to figure out which motor mount is bad...

Random misfire like that could be a bad ICM, check the ground under it. Start by checking your front motor mount.

Will do and the front motor mount is the one the dealership changed. However I get this loud squeaky noise every sense so maybe I'll take it back to them for a look see...

Did you ever fix this problem with the engine hesitation?
If yes, what was it. It describes my very problem exactly.

Welcome to the forum Dan. This post is 4 year old and I don't think you will get a reply from those guys, as they have not been on here in quite a while.
For better results, may I recommend that you create a "New Thread" in the Buick section, describing your problem on your 2000 Buick Regal. I am sure we all can help you out better then.