Hi Kai,
With one less factor, it's simpler, and the design can proceed as a simple 2x2 repeated measures. Please, see here:
Even though there are twins, it seems you only have MZ and DZ pairs, and so, differently than the HCP, that has more complicated sibships. This means it isn't strictly necessary to define, by hand, the multi-level exchangeability blocks. A simple column, with whole and/or within-block permutation is sufficient (internally PALM will create the multi-level structure, but it doesn't have to be specified by hand).
In the updated design, design1 is for H vs. L, and for the interaction of performance with zygosity, whereas design2 is for differences associated with zigosity while taking differences in performance into account. The design1 uses within-block permutation, whereas design2 uses while-block.
Hope this helps.
All the best,
Anderson