The route via Lucerne and the Brünnig pass takes longer time, about 4 hours and 20 minutes, compared to about a bit less than 3,5 hours via Berne and Zürich. However, the route via Brünnig is nicer.
The Bernina Express leaves Chur at 08:28 so you'd have to leave Interlaken at 04:58 -> way too early!
However starting 11th May there is a second daily Bernina Express leaving Chur at 13:28. Plenty of time to reach Chur via Lucerne and Pfäffikon SZ casually (or faster via Bern) :
- IR Interlaken Ost - Lucerne 09:04 - 10:55
- IR70 Lucerne - Zürich HB 11:09 - 11:50
- IC3 Zürich HB - Chur 12:07 - 13:22
- BEX Chur - Tirano 13:34 - 17:59
(Luzern - Pfäffikon SZ is beautiful too but you'd have to wait too long.)
Anyway there are hourly regional trains on Chur - Tirano enabling you to be flexible. Straightforward same-platform changes in Samedan and Pontresina or little detour via St. Moritz. :)
If you want to search connections via Lucerne add via Lucerne in the planner. And please use SBB app instead of the unreliable Rail Planner.