Hi casper,
As far as I understand, the user that created the spaces will have full access no matter what. As the user who created the spaces Engineering and Planning go to each space in turn. In More Actions choose Manage Space User. Select groups in the combobox and then show all. From here you can choose which GROUP has access and which ROLES they have.
IMPORTANT: In each of the new spaces uncheck the Inherit from parent space.
Finner