Our facility has recently "merged" with a sister facility. We have 76 sister plants in the US and a total of over 150 world wide. As part of the merge, we were informed as salary exempt employees that many of us would be laid off due to combining of positions with the sister facility.

So when the letters started coming out early this week, it was no great surprise. I have not personally been given a letter to date, but have been shown the letter by a co-worker who was laid off. The letter states that by signing the letter you agree not to ever apply at any other XXX facility at any time in the future. You must sign the letter to get the severance package. If you do not sign, then you will receive nothing.

Is it legal for an employer to mandate where you can and can not apply if it is not a "with cause" termination, and only a restructure lay off?

It is legal for an employer to include such language in the severance letter. If you don't wish to be bound by such a restriction, it is legal for you to refuse to sign the letter and waive the severance.