What I can more or less guarantee for the not too distant future is a conversations view that shows all tweets from the current one up to the root one - if the displayed one is a reply.

If the displayed one is a "root" tweet and you want to see all replies to it, it will be a little bit complicated as there is no API for that. I'll need to implement a workaround that will most certainly only work if the displayed tweet is not older than 7 days. And even then, the view won't include all results as the search API only operates on a partial set of the tweets from the last week...