What is the best option that's going to be safe for children/pets and require the least amount of reapplication?
I'm looking for something that has little to no phytotoxicity between plant species.
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Spray the plants with soapy water; a natural vegetable-based soap will work fine (no more than about a tablespoon per 2 liters of water). Make sure to spray the undersides of the leaves too.
However, do first check for ladybugs or other aphid predators; if there are any such predators present, there is no need to spray at all (and the soap would kill them too).