If your son spent more nights with you then you are the custodial parent and can claim the EIC and child care credit as well as file as Head of Household if you are unmarried. You would give her the signed 8332 to allow her to claim the dependency and child tax credit. 

What if somehow she claims him too and I get in an audit with the IRS?

The idea is that she does claim him for the dependency because you gave her permission to do it. You are not claiming the dependency. 

It feels tricky with technically 50/50 on paper.

You have to coordinate with her.