An L-2 spouse is employment-authorized incident to status and may work in the United States, including self-employment, subject to state licensing rules for the activity. A home daycare in particular is regulated by state and local rules that are separate from immigration permission.
Separate immigration permission from licensing
Immigration law answers one question for the spouse: may they work. For an L-2 spouse the answer is yes, without a separate employment authorization document, and it applies equally whether the principal holds L-1A or L-1B. Whether a particular business can operate is a different question governed by the state and municipality, and a home daycare will need licensing, inspections and often background checks that take time.
Sequence the move so the spouse can apply for those permits after arrival rather than promising clients a start date. Children in L-2 status can attend school but cannot be employed, and each dependant's status ends when the principal's does, so the five-year cap on L-1B is the household's planning horizon. Keep the Québec daycare's closure, any provincial permit and the spouse's tax position on the household timeline, since Canadian obligations do not stop at the border.