Bharatha

Bharatha is son of King Dushyanta. Shakuntala is  his mother. Our country is called Bhaarata or Bharatha khanda due to this Bharatha. 

Shakuntala is the daughter of apsara(angel) Menaka. Sage Kanva was bringing her up. King Dushyanta sees her and he falls in love with her. He courts her and marries her in the forest. 

Then king returns to his capital. After few days, when Shakuntala, by then with a child, goes to Dushyanta's court, king had forgotten her completely. Due to a curse by sage Durvasa. Rejected by her husband,  Shakuntala comes back to the forest where son Bharatha is born. 

Few years later, King comes to forest, recognizes Shakuntala and Bharatha and takes them back to the palace.

Bharatha in Ramayana

Bharatha in Ramayana is the son of King Dasharatha and Queen Kaikeyi. When the king is planning for anointment of Crown prince Rama, Kaikeyi reminds Dasharatha of 3 wishes he had granted her. 

Now she wants them and she says her son must be crowned and Rama must live in forest (Vanavasa) for 14 years. Bound by his promise but at the same time not able to withstand the separation from his favorite son, Dasharatha dies. Lakshmana, the second son wants to go to vanavasa with Rama. 

Bharatha who was in his grand parents house, comes back and hears the events and is very angry with his mother. He runs after Rama requesting him to come back and rule Ayodhya. Rama  is not ready to go against the promise given by his father. Bharatha brings the foot wear of Rama and keeps them on throne and rules on behalf of these. 

Mohini

In Sagara manthana:

Gods and demons decided that they want to bring Amritha (nectar) from heavens. For that they were supposed to churn ksheera sagara (ocean of milk).

How big a rope do you need to churn the ocean? When gods and demons were discussing that, it was concluded that Vasuki, the lord of snakes will be the rope and the mountain Meru parvata will be the trunk.

But once the churning started, Vasuki and mountain started sinking. Then Vishnu  took his incarnation as Koorma or turtle and supported Meru parvata.

Demons argued and got to hold Vasuki's head and Gods held tail. Due to poisonous breath of the serpent many demons died.

The first thing to come out of ocean was not nectar but  very powerful poison called halahala. It was so strong that all living would have died.

All the gods requested God Shiva and he swallowed the entire poison to save world. His wife Parvati, stopped the poison from entering his stomach by pressing his throat.

After halahala other things came out of ocean. Lakshmi was one of them whom God Vishnu married. Then there came kalpavraksha and kamadhenu, a tree and a cow which would fulfill all wishes.

Finally nectar came. By this time demons were infuriated as they had nothing so far. But giving nectar to demons will make them very strong and they will never die. And hence cause havoc on heaven and earth.

Some scheme was to be evolved to avoid demons from getting nectar. For this Vishnu took the form a beautiful woman and appeared in front of fighting Gods and demons. This was Mohini.

Mohini offered to distribute nectar among equally. She asked them to stand in two different lines - one of gods and one of demons. Bewitched by her beauty, all agreed to this.

She kept on poring nectar to gods and by the time she finished their line nectar was empty.