An L-2 spouse is employment-authorized incident to status, so he may work for a US employer once admitted in L-2 status with the appropriate I-94 annotation. Whether he can continue a Canadian trades job depends on where the work is physically performed; work done from US soil for a Canadian employer is still US employment, but as an L-2 spouse he is authorized.
Check the spouse's authorization, then the trade's licensing
The L-2 spouse's position is comparatively favourable: since USCIS policy recognized spousal employment incident to status, an L-2 spouse admitted with the spouse annotation on the I-94 may work for any US employer without a separate employment-authorization document, although some employers still ask for one. The immigration question is therefore settled early. The practical question is the trade itself.
A Quinte West electrician, plumber or gasfitter cannot rely on an Ontario certificate to work in most US states; licensing is state-by-state and often requires local examinations and documented hours. He should contact the licensing board in the destination state before the move, since reciprocity varies and some boards accept Canadian apprenticeship hours while others do not. Children in L-2 status may attend school but are not employment-authorized, and any child approaching twenty-one should be calendared, because L-2 status ends at that age.