No. The same L-2 rules apply regardless of location — a qualifying spouse is employment-authorized incident to status, while children do not gain work authorization through L-2 status alone.
Apply the standard dependent rules regardless of location
Record each family member's citizenship, relationship evidence, and intended activity the same way this would be done for an urban assignment. A rural or small-town posting in the United States does not change any dependent's legal permissions.
Prepare a separate status plan for the transferee, spouse, and every child, including passports, relationship records, intended travel dates, schooling, and work plans. The rural location of either worksite changes none of the dependent rules. L-2 spouses are employment-authorized incident to status; a spouse should still retain evidence of the admission classification used for employment verification. Do not imply that children receive the same work permission merely because they hold dependent status. The common planning failure is arranging a spouse's start date or a child's activity before confirming admission records, while overlooking that the principal's L-1B eligibility rests on the qualifying relationship, foreign year, and specialized-knowledge assignment.
Hypothetical example: An irrigation-pump designer from the Strathroy-Caradoc area transfers to teach an affiliate's proprietary testing method. His spouse plans remote accounting work after joining him, while their university-age daughter intends to study. The family checks each person's classification and documentary needs separately. The spouse relies on valid L-2 spousal status for employment authorization; the daughter does not assume that her dependent classification supplies identical permission to take a job.