Lunar Isolation 1:13

Luna may be emotional but she's not a child. Celestia is her sister, not her mother. Celestia has no real power over Luna, if Luna wants to leave then she can just leave. That's why Luna functions as a check on Celestia's power, she's the one pony that Celestia needs to keep on her side. That's how the equestrian political system functions.
Luna's usual portrayal is as very independent. Though she appreciates friends she prefers to run risks herself and rules by the motto "if you want something done right, do it yourself". Actually 'do princess dream of magical sheep' does show some aspects of that; her insistence to do it by herself and her referring to her subjects as "my friends".