Why are Telugu people able to dominate Karnataka and Tamil Nadu politics but not Kerala politics? How is Kerala effective in stopping Telugu grain from getting boiled in Kerala?

 

1. Contrary to what you have stated, Kerala was very much under Vijayanagara Empire.
2. Travancore became feaudatory after Kumara Kampanna, Son of Bukkaraya, defeated Madurai Sultanates in 14th century. Tenkasi Pandyas become Governors on behalf of the Empire.
3. Malabar became feaudatory and annexed to Mysore.

When the famous emperor Krishna Devaraya was ill, there was a rebellion in Chozha country; Travancore attacked and defeated Tenkasi Pandyas, occupied Tamirabharani region, Malabar declared independence.

There was a considerable delay due to change in reign and Jadavarma Pandyan of Tenkasi sought help from the new emperor Achuta Devaraya.

He made the expedition.

1. With Chozhas hiding, Achuta Devaraya made his commander Sevappa Naicker as the King of Thanjavur and it give birth to Tanjavur Naicker Kingdom. During his stay, he Achuta Deva Raya offered his Sister in law to marry Sevappanaicker. Thanjavur as well as Mysore Kingdoms were loyal to the empire till it met is due to their marital alliances.
2. One of the houses who supported the dynasty, Ravillas were made Governors of country lying between Travancore to Calicut, though it did not last more than 5 decades. Currently the descendants are in Ilayarasanendal, Tirunelveli.
3. Achuta Devarayas army went with his brother in law Saluka Pedda Tirumala (brother of Patta Mahishi Varadamma) defeated Travancore and made it to a feadatory. Pleased Pandyan Jadavarman SriVallabha offered Tenkasi Princess as Third Raja Mahishi to the emperor.

Kerala under Vijayanagara Empire but two different regions were annexed to other feaudatory kingdoms.

Meanwhile, after defeat of Talikota in 1547, it changed the capitals to Penugonda, Chandragiri, Vellore and ended in 1646 with Sri Ranga- an emperor with no empire, but its feaudatoris last long.

Source: Achuta Devarayas Military Expeditions.

PS: Achuta Devarayas second wife is a Sanskrit Scholar (Sister in law of Tanjore King) raised to the ranks of Raja Mahishi, due to her commentary on his rule.