Q:

whether + infinitive

I am not sure how the construction "whether + [infinitive verb]" is used. Examples:

I don't know whether to turn left or right. (= I don't know if I turn left or right ?)
I don't know whether to turn left will take us to the hotel. (= I don't know if turning left will take us to the hotel )

Are these two sentences gramatically correct? Do they have the meaning inside the parentheses? 

A:

Original A: I don't know whether to turn left or right. (= I don't know if I turn left or right ?) 

The first version is fine. There needs to be a "should" in the parenthesis version. 

I don't know if I should turn left or right.

Yes, they mean the same thing. Note that there are only two options here, you either go left or right (in B you have three options).

Original B: I don't know whether to turn left will take us to the hotel. (= I don't know if turning left will take us to the hotel )

Note that if you just write left (instead or "left OR right") then you are saying "... should I turn left, right, or keep going straight... (unless there is no straight path and the road splits in opposite directions). 
The following is how I would say it (BillJ in his comment says the same thing). 

I don't know whether to turn left to get to the hotel. OR, I don't know whether turning left will get us to the hotel.

