Insisting on no-contact isn't a "demand," it's a boundary (or it isn't, depending on whether or not you're willing to live in an open marriage).
Insisting upon full transparency is but tangible evidence that the boundary isn't being violated.
Your IC has it precisely BACKWARDS. You'll never GET your wife "back" if she continues to have contact with her OM. The NC comes first (enforced by transparency), while the two of you slowly piece your marriage back together.