His wife may enter in L-2 status and is employment-authorized incident to that status, so she may work without a separate permit. Children under 21 in L-2 status may attend school but may not work, and everyone's status ends when Owen's L-1B ends.
L-2 rights do not depend on whether the principal is L-1A or L-1B
The spouse and child rules for L-2 are the same whether the principal transfers as a manager or as a specialized-knowledge employee. Owen's wife could take employment with any U.S. employer, work remotely for a Canadian employer from inside the United States, or start a business, relying on the annotated Form I-94 as evidence of authorization.
His children, if unmarried and under 21, could enrol in school. An eighteen-month assignment may be extended, but the five-year L-1B maximum applies to Owen and therefore to the family. A child who will turn 21 during the placement should have a separate plan.
If Owen's wife holds only Canadian permanent residence rather than citizenship, that does not affect L-2, which is available to any nationality.