What is the shortest route by time to get from Varenna to Interlaken> Is there a ferry that takes you to Lugano and you go up or do you have to return to Milano to get on the right train.
There doesn't seem to be an easy way to make this run. Trenitalia runs will all take you back to Milan and then north to Spiez and then Interlaken. All runs take 6.0hrs. A second choice is to take the ferry across the lake to Menaggio and then take a bus to Lugano. This should consume about 90 minutes. At Lugano, you are in Switzerland the the Swiss train network shows runs that go through Luzern to the north or west through Locarno, Domodossolo and then north to Brig, Spiez and Interlaken. The Luzern run takes 5.0hrs with one train change. The Locarno/Domodossolo run takes 4hrs. 45min but it has 6 train changes. Big mountains between Lake Como and Interlaken.
The advice given by Larry seems wise. Just be aware that there are two RR stations in Interlaken. When you arrive go to the ticket window and ask about how to get where you want to go.
When you buy your ticket, ask the clerk for a computer printout of your itinerary so you will know the train numbers, departure times and towns where you change trains. Having a copy of your trip helps a lot.