Even without the temporary project Berlin-Vienna-Munich-Interlaken is a more sensible routing because it avoids huge amounts of doubling back.
Best day time options are depart Berlin Hauptbahnhof at 07:28 or 09:28, around 4 hours travel then change at Prague (about 70 minutes transfer time) then about another 4 hours to Vienna. The earlier departure is currently about €30 per adult cheaper. Both departures from Berlin and the earlier from Prague are new(ish) Czech trains with well priced restaurant cars for breakfast/lunch https://www.jidelnivozy.cz/uploads/menus/foodMenu/1.pdf the later departure from Prague is Austrian, basically the same sort of train but more expensive restaurant! Cheapest tickets are booked early at bahn.com - book as a through ticket Berlin-Vienna, you may need to add Prague as a stopover to fix the route.
Vienna-Munich is simple, rather oddly Westbahn (the "cut price" alternative operator) has flat rate fares which only make sense once the DB/OBB trains have sold out of early booking tickets (bahn.com again).
I've never stayed in any of the cities, having visited from elsewhere, try using the www.HRS.com booking site which specializes in Germany and not just the high priced places, you can select three star (or even 2 star) to keep prices down.
Munich-Interlaken should be via Zurich, bahn.com will try to offer a few slightly cheaper options which involve a huge detour in Germany which may be a difficult connection - again buy it as a through ticket, in fact if you do stay in Wengen buy it as a through ticket to there, the price may be teh same as Interlaken!