A and B are opposite statements. As you say, in standard English two negatives usually cancel each other out resulting in a positive. However in certain cases (often called double negatives, but that distinction is not always followed) the negatives are reinforcing or emphasizing. This is more common in colloquial English.
In the case here, A has a single negative, B has two negatives. They are opposite statements in my interpretation.
A is however not standard or acceptable English.
B is acceptable standard English English, also the following is acceptable English that has essentially the same meaning, with the negative moved.
There isn't anywhere I'd rather be than here with you.
An example of reinforcing double negatives include Pink Floyd's Another Brick In The Wall, that includes the line:
We don't need no education
.. but this is clearly colloquial rather than standard English.