Could I get her fired?

There's a reason why the term "slap on the wrist" means something that counts for jack squat. She might have done it hard, or soft, (you left it kinda ambiguous). The fact of the matter is, she didn't go as far as aggravated assault, just a slap on your arm. You were conflicting with her religious views. If you and your co-workers keep up your juvenile behavior of constantly swearing in front of her just to tick her off, she would have every right to bring a hostile environment suit against YOU.
Look at it from her perspective:
A prepubescent swears loudly "GodDammit" with no sense of the actual meaning behind the word. Being religious, you slap him on the arm, as it is rather offensive to you. This same person is now egging other people on to do the same thing to shock you further.

 

Deathsnovas advice: Ignore her.
Why would you try and hurt her by going around and saying 'God damnit'
You arnt 12 years old, grow up.

 

You can't get her fired, sorry. Just ignoring to her.