Your siblings is not a reproductively isolated population (hopefully=)). The relevant question is if the helpers are more or less fit relative to the population as a whole. So in your example, where the helpers give up something and get back less, the gene goes extinct.
But start instead of just zero-sum redistribution with something like that trust game where you send money through a slot and whatever amount you send the other guy gets triple. But it's multiplayer and simultaneous. So the helpers give up some amount, let's say x each and every family member gets three times what the average participant gave up. If half of the family members are helpers then everyone gets 3x/2. Which is more than x, so now the gene gives a fitness advantage.
Here is a toy model:
Let's ignore the details of genetic reproduction, and simply assume that if both parents have a trait, all children have it; if no parent has a trait, no children have it; and if one parent has it, exactly 50% of children have it. Let's assume all families have the same size. (These are quite unrealistic assumptions to make calculation simple.)
Let's suppose that being nice to all your siblings has a cost c (for example, if without reciprocation it would reduce your survival rate by 5%, then c = 0.05), and that being supported by all you...
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