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There is nothing to decompose with respect to $$\mbox{SL}(2,\mathbb{C})$$ because the spinor tensor with one undotted index and one dotted index is irreducible. Actually, you should write it backwards and apply the same rules as you already did for the 1-form representations:
$$\left(\frac{1}{2},0\right)\otimes \left(0,\frac{1}{2}\right) = \left(\frac{1}{2},\frac{1}{2}\right)$$, and this because $$\frac{1}{2}+0 = \frac{1}{2}-0 = \frac{1}{2}$$ for both terms.