Yes every country's independence movement saw violence, but LTTE here just killing the innocent people. Initially LTTE's main goal was Tamil's benefit, but later LTTE become more like terrorist organization with many of the brutal terrorist attacks.
I think the best way for peace in Srilanka would be to involve India actively in peace talk and both of the part *Sri Lanka & LTTE) must agree what India tells. But for some reason LTTE is not agreeing so srilanka also says no.
as far as relation with neighboring country is concerned for India, the actual problem is the Indian leaders they don't have any vision they are too busy making money and grabbing power, where is the time for them to think about country.