@acjay there definitely is a way to do it. You could have a switch either as 3 buttons or a handle to activate the various options. The three buttons might be easier to child proof, where technically only the hot water would need to be proofed.
The technical part mainly happens below the sink. The three outputs would need to be merged together before pouring out of the faucet. The switch would be used to open and close the valves before merging.
@acjay yes that would be the best approach. Otherwise the parts should be available at larger home department stores.