Is it suitable/permitted to use は twice when relaying what someone else said?
E.g:
ロバートさんはお母さんは料理するのが下手だと言っていました。
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Sign up to join this communityYes it's perfectly suitable. The quote part (marked with と) is an independent sentence and can have another は.
Another situation where you have two は's is when you want to use は as an explicit contrast marker (e.g., 彼は背は高い "He is (at least) tall").