This sentence is quite tricky to translate into Russian indeed because Russian words for "to want" and "to like" don't work like their English counterparts.
If we consider several other English sentences with exactly same grammar:
- They teach her to beat him
- They send her to kill him
, they could be translated into Russian simply as
- Они учат её бить его
- Они отправляют её убить его
, which are perfectly grammatical if somewhat peculiar (or not, depending on context) Russian statements.
This is because English verbs "to teach (someone to do something)" and "to send (someone to do something)" are trivalent, meaning they can have three arguments ("they, her, to beat" or "they, her, to kill"); and verbs "to beat" and "to kill" are bivalent, that is having two arguments ("she, him").
The same holds for Russian verbs учить (кого-то делать что-то), отправлять (кого-то делать что-то), бить (кого-то) and убивать (кого-то).
This is not the case for the verbs нравиться and хотеть.
Хотеть in Russian is bivalent. You cannot "want someone to do something" in Russian, only "want someone" or "want something". If you are about to say that you want ALICE to FOO in Russian, you in fact say "I want something", and this "something" is the situation where ALICE does FOO. You use a subjunctive sentence: "I want so that ALICE did FOO".
Нравиться is tricky too, because it's, first, reflexive, and, second, impersonal. It's exactly the same grammar as in Spanish me gustan las manzanas ("myself taste the apples") for English "I like apples". So Russian for "he likes her" would be ему нравится она, which grammatically is "to him wills herself she".
This, again, is not something a Russian speaker would analyze when speaking. It's just a way to tell this in Russian, in the same way as it is in Spanish.
If we combine the two verbs above, we'll get:
Они хотят, чтобы она ему нравилась
, making a subjunctive sentence for "he liked her" and using that as a single possible object for хотеть, "to want".