P2U is exactly correct.
The more independent the left hand is, the more comfortable you'll be in these type passages.
Since most people are right handed, and since most of the work in piano is done by the right hand -- at least the difficult work -- this leaves the poor left hand quite neglected.
So I agree that the left hand needs to be MORE competent than the right hand!
Beethoven is simply chocked full of these type of passages i.e. tremolos of one sort or another mixed with Alberti type bases... just to cite a few... 3rd movement of Moonlight, 1st and 3rd mvmt of opus2 no 3, 1st mvmt of Appassionata, 3rd mvmt of Les Adieux
What I have done is make a little routine of playing all sorts of these left hand tremolo based passages mixing them together in all keys building endurance. (the Hanon tremolo exercise is actually pretty good but deadly boring and I don't think its as good as doing a lot of mixed salad Beethoven bases!)
Also, do all finger combinations of trills with the LH, since all a tremolo is, is a trill in a wider expanse!
Start doing say 5 minutes of a variety of these bases left hand only in a comfortable tempo, say 20% or so less than your "discomfort" speed, until you can change at will into any key and any configuration.
Once your LH feels like a real foundation upon which the Sonata rests (not struggles with) then you've really accomplished something.
I'm afraid there is no easy way, trick, or quick way around this.
And if you really dedicate yourself to doing this every day and make LH work alone part of your routine, you'll be amazed at how your technique and confidence will improve.
A strong and independent LH is a MAJOR asset for pianists!