“Let Bharata be fine and may Rāma be happy” means “Let Bharata and Rāma be fine and do whatever They want!”

NOTE. These statements are generally symptomatic of the conditioned souls’ forgetfulness of service to the Lord. Prabhupāda describes the factual position of the conditioned souls vis-à-vis the Supreme Lord thus:

The constitutional position of a living entity, represented by Arjuna, is that he has to act according to the order of the Supreme Lord. He is meant for self-discipline. Śrī Caitanya Mahāprabhu says that the actual position of the living entity is that of eternal servant of the Supreme Lord. Forgetting this principle, the living entity becomes conditioned by material nature, but in serving the Supreme Lord he becomes the liberated servant of God. The living entity's constitutional position is to be a servitor; he has to serve either the illusory māyā or the Supreme Lord. If he serves the Supreme Lord he is in his normal condition, but if he prefers to serve the illusory, external energy, then certainly he will be in bondage. In illusion the living entity is serving in this material world. He is bound by his lust and desires, yet he thinks of himself as the master of the world. This is called illusion. When a person is liberated, his illusion is over, and he voluntarily surrenders unto the Supreme to act according to His desires. (Bhagavad-gītā 18.73 purport)