Why didn't Baahubali seek Kunthala Kingdom?

There are few things we have to consider.

1. Baahubali is not banished from the Kingdom but only from the palace.

   We should remember that Amarendra Baahubali and his wife Devasena were not banished from Maahishmati Kingdom. He was banished from the palace. By this punishment it means that he has permission to live in Mahishmati kingdom but should not live in a palace. Let it be any palace, Kuntala or Mahishmati.

2. Making a convict as the king is taken as revolt against the emperor.

   This punishment is sentenced by Raja Mata Shivagami Devi. She is the head of the Mahishmati empire. Kuntala is just a small kingdom affiliated to the Mahishmati empire. The punishment or an order given by the empress(well Shiva gami has more power than Bhallala Deva when she gave the sentence). So, her punishment must be obeyed by all the kingdoms affiliated to the Mahishmati Kingdom. So, Bahubali and Devasena should not be given a shelter even at the Kuntala kingdom as they are convicts. Convicts will not be given the throne according to the ancient rules. It will be counted as Rajya-Dhikkarana meaning going against the king or the Kingdom. If done thus, Bhallala Deva would destroy the Kuntala kingdom. (He did it after Shivagami left with Mahendra Bahubali only because they gave support to Baahubali and Devasena rejected him).

3. Patriotism of Amarendra Bahubali.

   Amarendra Bahubali is the greatest known patriot of his motherland. During the war with the Kalakeya clan, he gives an inspiring speech to the soldiers in which he was ready to die for his motherland. Even at his last moments, he said Jai Mahishmati. This shows how much devoted to his motherland. So, we cannot expect him to leave his motherland just for his comfort.

4. He was following Hindu tradition and keeping his word to Devasena.

   According to Hindu tradition, it is the husband who has to take care of the wife what ever it takes. The bride's family will not take give support to the family. There is no rule that they should give shelter during their hard times. But there is no rule they shouldn't. This is the reason Kumara Varma and Devasena's family are seen along with Baahubali in the film. But the feeding and taking care of the household will be solely on the groom(husband). It is a promise given by the Bride to the groom in the form of a ritual in a marriage. Besides, Amarendra Baahubali promises Devasena that he will take care of her until the death separates them. SO, it is his duty to take care of Devasena.

Not to forget that Amarendra Baahubali is a noble warrior. If he seeks Kuntala Kingdom, it makes him dependent of others. This reduces his nobility.

Hence, due to above reasons, Baahubali did not seek Kuntala Kingdom when banished.

Kunthala kingdom is occupied by Mahishmathi king Baahubali during his ruling time as king. So Kunthala kingdom also belongs to the one who is ruling Mahishmathi. Now since Bhallaladeva was the king and Baahubali was banned from the kingdom, it means he is banned from every area that comes under the control of the ruler. So Baahubali is not left with Kunthala kingdom.