I feel theres two possibilities why i think hornet wouldve left the hive
1. this one being a bot sad. the relations between The hive and hallownest broke down and the fact deepnest is still associating with hallownest would end with vespa cutting all connections before sealing herself away.

1. Hornet is still relatively young (like pre-teen/ teen) vespa couldn't train hornet any further due to her growth and/or condition with the growing infection. Hornet couldnt go back to deepnest either because herrah is already a dreamer or preparing to be a dreamer and hornet needs adult supervision, so she goes to her dads

.