A parent and child item pair will just be shifted along the axis, not mirrored.
Steps to reproduce
1. Open attached scene. 2. Select the cube item in the item list (the sphere is parented to it, so you don't need to select the sphere as well). 3. Duplicate > Instance Mirror (click and hold on the Mirror button). 4. Make sure the Item Effector > Parent dropdown is set to Off. 5. Make sure the Item Effector > Hierarchy box is checked. 6. Make sure the Mirror Generator > Axis is set to X. 7. Click apply.
Expected result: Modo will mirror the cube and the sphere across the X axis.
Actual result: Modo creates an instance of the cube and the sphere, but they're not mirrored. They're just shifted along the X axis, so the sphere is on the origin.