In general, in a negative question, do you expect the negative particle thingy eivät (I don't know its proper name) to be separated from the other part or the verb? I notice if "sinulla" comes first, it separates the verb parts, and if "sandaalit" comes first, it separates them, but then "sinulla" moves to the end.
Hmm, very good question.
"Ei" is, weirdly enough, a verb. "Eivät" = (they) do not, and "-kö" is a question particle. So "eivätkö" is the question "do they not?".
In this sentence, you start with that "do they not?", and I guess then you have to continue with what they refers to = sandaalit. Then the verb (ole), and then the new information (sinulla = sinä in the adessive case, literally meaning "on you" but carrying the meaning to possession, "by you").
In the other sentence (which I assume you meant), you start with the negative verb + the question particle (Eikö), then the person we are talking about in the adessive (sinulla), then the verb (ole), and then the new information (sandaaleja, sandaalit in the plural partitive).
So both follow the same structure as the positive statements (Minulla on sandaalit and Sandaalit ovat minulla), but with the negative question in the beginning of both. I don't know if this dissection is of any help at all. We may need to look at more complex sentences to see which words end up where...
Eikö sandaalit ole sinulla? is wrong because you need the plural verb for the plural sandals. In the spoken language you miiiight hear Eikö sandaalit, but then the other words probably wouldn't be pronunced properly either, and it would be more like Eikö/Eiks saandalit oo sulla?.
Eivätkö sandaalit ole teillä? is another correct option and accepted here.