Try to get your facts straight before making wild allegations.
1. The british unified the current nation state of India and this feeling of "national unity" is just that "a feeling". Even separate nations in Eurpoe don't kill neighbors over river sharing disputes now. India as a single entity is good for trade and defense, but it is good for each ethnic group to maintain its own identity. Tamils retaining their own culture and language is not a threat to India, but should be seen as the example for the future for all ethnic groups of the sub continent.
2. The Tamils seeking a separate state in Ceylon/Sri Lanka did not move there from the south of the Indian subcontinent. The south eastern part of India and the North Eastern part of Ceylon/Sri Lanka have been Tamil Homelands for unknown periods of time. When the British colonized India and Ceylon and then gave these countries independence, the Tamils in India got a state, the Tamils in Ceylon didn't get that even. They tried to coexist with the Sinhalese majority but were brutally attacked and that resulted in the call for a separate nation called Tamil Eelam.
3. The IPKF sent by Rajiv did not help the Tamils. It was sent to destroy the LTTE and bring Sri Lanka directly under Indian influence.
4. The clash between Karunanidhi and the VHP/other Hindu outfits is not a Tamil vs Non-Tamil issue. Traditional Hinduism annexed a bunch of other religions to bolster its numbers. These annexed religions do not recognize Ram.