GOOD: We shouldn't give children whatever they want. We shouldn't give children everything they want. CONFUSING/AWKWARD: "anything they want can't be given"? If you really want to use passive voice (though generally you should avoid it): "Children should not be given everything /anything/whatever they want"

The sentence means this: "Not every request a child might make should be granted." Your suggested alternative meaning is not valid because "anything" does not express the randomness of "whatever". "Whatever they want" means any notion that may randomly pop into their mind, or every whim. "Anything", by contrast, expresses no randomness, so it is an entirely different idea.

Not ambiguous: We shouldn’t give children whatever/everything they want. We shouldn’t give children anything they want. Ambiguous: We shouldn’t give children what they want. (It’s a good sentence but the meaning has to be clarified by the context)

Theoretically, the sentence "We shouldn't give children whatever they want" could create confusion because "whatever" can mean "anything" in some contexts. This might lead someone to (mis)interpret it as "We can't give them anything they want at all" (which is an extreme, absolute interpretation). However, in everyday English, the intended meaning—"We shouldn't give children everything they want"—is much more common and natural. Context usually makes this clear. To avoid theoretical confusion, you could rephrase it as: "We shouldn't give children everything they ask for." or "We shouldn't always give children what they want." These versions remove ambiguity entirely.

If you want a really natural way to say this using a common idiom natives will understand, you can say: Children shouldn’t have everything handed to them on a silver platter. It conveys the idea that children should learn to work for the things they want otherwise they will be come ungrateful and/or lazy. Hope that helps.