I then asked her if we could discuss bills. We sat down and I calmly went over the monthly outflow, and she took notes as we did some discussion of what she needs to be responsible for. She didn't seem to be too stressed about it, but it added up to almost double her take home pay monthly.
This is a good way to apply some pressure, but you'll have a tough time enforcing it if she chooses not to perform. She may just call your bluff and let the bills go unpaid (that's probably what her lawyer advised). As the primary income earner you could be faced with the choice of paying or suffering derogatory credit statements.
She has you in a tough spot right now. She has a place to live, access to the children and can come and go as she pleases. You'll pay the mortgage and other necessary household costs for the sake of your children and your own future. You don't have much leverage without proceeding legally.