The pattern I see most often with dependent applications specifically: it's rarely the visa application itself that stalls things, it's a supporting document that needs authentication you didn't expect — birth certificates and marriage certificates especially often need an apostille or certified translation that takes weeks to arrange, and people start that process too late because they assumed the "main" applicant's paperwork was the priority.
My advice: treat every dependent's documents as their own mini-project with their own lead time, starting as early as the primary applicant's. The Immigration section of your destination's guide will usually flag exactly which supporting documents need authentication.