Because if it rains tomorrow, I will get wet, I hoped for a sunny day.
Okay. It's fine-ish.
The tense seems a bit odd. You are talking about a possibility for the future (relative to now?) and of a hope in the past.
That's not wrong. It would make sense for example if someone had just told you (today) that there was a forecast of a strong chance of rain. The rain remains just a future possibility, but the hoping was done in the past, so all the tenses work logically.
It's just not a very likely combination of tenses, so standing on its own, without the context of such a forecast, it strikes me as odd, where it wouldn't just after such a forecast or some other reason for the unusual tense combination.
So let's change the tenses just so I'm no longer distracted by that!
Because if it rains tomorrow, I will get wet, I hope for a sunny day.
Can I follow that? Yes.
Is my understanding of if what you wanted it to be? I'm pretty confident it is.
Do I at any point get tripped up, and have to mentally backtrack to understand you? No.
Can I see any grammatical problems? The first comma isn't wrong, but isn't necessary either, and I think you'd be better of without it, but I don't see any problems.
Can you start a sentence with two subordinating conjunctions? I'd say "yes" as a general point of theory, and I'd accept the above as evidence to back it up.
Is it a good sentence? Ah…
It takes me a while to get to your point.
Now, that's not in a terrible way. I don't get half-way through your sentence, realise I misinterpreted a clause and have to go back and start again.
But it's generally not a good thing either. There's a lot of build-up to just the hope of a sunny day.
But it's not always a bad thing.
It happens with any Because sentence, and the if adds to the effect. Consider:
Because the Origami didn’t work
We gave you dancing lessons
Because the dancing lessons made you bored
We bought you a guitar
Because you said
It made your fingers sore
We found you a pony
Because the pony broke your leg and ran away
We got you drums
Here the fact that putting the subordinate clause first leads us along for a bit before we get to the main clause is the whole reason this song works.
Your "Because if" structure increases the "leading along" quality, but the pay-off doesn't seem to be worth it.
And of course example sentences are rarely those with the best punch. (It's hard enough to think of a good sentence when writing, or a valid example when examining grammar, so doing both together is really tough). The actual form of "Because if…" I'd say is fine, I'd just better get something after it's done leading me through the subordinate clause.