No. The citizenship requirement applies to the TN principal applicant, not to dependents. A spouse and unmarried children under 21 may qualify for TD whatever passport they hold, though the procedural steps before travel differ according to each person's own nationality.
Nationality changes the route, not the eligibility
First determine whether the child needs an immigration classification at all: a US citizen does not need TD. For a non-US citizen, confirm TD eligibility and any visa exemption using all citizenship and current status facts. A Canadian passport may support a different process from a sibling’s, but passport nationality alone should not be used to invent a universal rule for everyone else.
Put a name beside each determination. One adult should confirm, for every child, three things: the citizenships currently held, whether any of them is American, and what the applicable procedure requires for the passport that child will actually present. Where the answers differ between two children, record both rather than reconciling them into a single household rule.
A consular officer decides the visa question for the child in front of them; an inspecting officer at the port of entry decides admission; neither is bound by what was concluded for a sibling. If nobody is assigned that per-child check, the family generally discovers the gap at the counter, where it can no longer be corrected.