United is about as dependable as any airline in the world. I think they do a pretty good job at most things (despite the hate some folks heap on them). One-stop to Dubrovnik is about as good as it gets between the US west coast and Croatia.
Book a single ticket with United, on United metal all the way (or on United and one of their European partners).
If you make your one-stop in Newark, United flies from there nonstop to Dubrovnik. If you prefer a long nonstop from SFO to Europe (all other things being equal, I'd certainly pick that), then connect in one of United's partner hubs (most likely FRA) and continue on the short hop to DBV. Easy and stress free.