I've thought that "tener la mano pesada" is a decent translation for "to rule with an iron fist" or "to be heavy handed."
Now for the expression "Tener la mano muy larga." If that means a person who hits people at the slightest provocation or is always wanting to fight (buscapleitos?), I might say "he's looking for a fight," "he's a bully," "he's authoritarian," "he likes to throw his weight around," "he's quick to come to blows," etc., though it depends on the exact meaning of what's intended with "tener la mano muy larga."
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If you find something wrong with my Spanish, please correct it!
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