Hopefully this clears up the confusion about the Indian support for Dalai Lama as you put it......
See India is a democracy, and I mean a democracy in a literal sense of the term.We have a constitution which guarantees
1) freedom of debate to everyone irrespective of whether it insults any country, individual , state , state representative , any form of authority , any institution .....
2) Freedom of political activity , holding processions , strikes ,demonstrations
3) Freedom of movement of all residents in any part of India, abroad ....
4) Freedom of meeting any individual , representative of government ,state dignitary etc.
and these rights are guaranteed to all including the Dalai Lama and every -one of his followers as it is to all Indians .
There is no way these can be taken away by the government , not even under exceptional circumstances , ( except maybe for a military emergency )....and certainly not on ordinary matters like in order to appease a foreign state . This is similar to any other western democracy in the world.
I 've already explained that expecting India to expel the Tibetan would be like expecting us to compromise on our national soveriegnty.
That which is in the power of the Government i.e stopping all armed activities overtly or covertly directed to challenge Chinese control over Tibet, declaring Tibet is an integral part of China ....has already been done by the Indian Government.
for instance during the Sri Lankan civil war , a huge number of people in the state of Tamil Nadu were against Govt policies on support to the Sri Lankan Govt and openly expressed their dissent.They could not be stopped from using their right of free expression.
Again , at the moment Barack Obama is in India and there are a huge number of communist party supporters against the visit who are holding demonstrations and expressing their disapproval. Neither can they be stopped from doing so.
Coming from a different political system in China where there is relative uniformity in both administration and opinion, it may be difficult to visualize why the Indian Government cannot "control Tibetan Protesters " like the Chinese government does many of its dissidents but that is a characteristic of our pluralistic and tolerant society .......and no government in New Delhi can do anything that contravenes this .
So officially we 've done all that could be done , but what you are asking is not within the power of the Government to do.....