Is it appropriate if I form a sentence by using two of these conjunctive adverbs like in the following sentence?
However, in spite of her attitude, he did well.
Is however quite redundant?
That's fine - depending on prior context. You don't start a single, standalone sentence with "However" - it's a statement to contrast the sentence with another. It is not redundant here, because "in spite" contrasts the two clauses within the same sentence: the attitude, and "his results". "However", however, contrasts the whole sentence with another sentence which might precede or proceed the one you wrote.
She said he had no chance to succeed and nagged him about it at every opportunity. However, in spite of her attitude, he did well.
In this case you have both negations applied fully: "However" opposes the first sentence, "In spite" - the first clause of the other.
If you use it like in your example though, without any sentences to contrast against, it's not redundant - it's just senseless.