The original sentence is
poor as it is ambiguous.
It can mean that you have problems at work, or that you can't take the project home to work on it:
Write, if you mean you have problems at work:
We are under the gun at work to get this project finished.
At work, we are under the gun to get this project finished.
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For the other:
We are under the gun to get this project finished, and we're not allowed to take it home.
We are under the gun to get this project finished, and we're not allowed to work on it at home.