No, it's not dative. It just a noun that gets endings like adjectives do (it declines like an adjective). There are many nouns in German that do this, often referring to people. Here is a good explanation.

After reading that link you might notice that verwandt is an adjective meaning "related", so when you talk about "a relative" you're kind of saying ein verwandter Mann or eine verwandte Frau, and we just leave off the noun and use the adjective as one instead (ein Verwandter or eine Verwandte). Hence when you have the plural, the ending depends on whether there's an article or not (remember the adjective endings pattern): Ich habe Verwandte but Sie sind meine Verwandten, for example.

You can study the full declension table for Verwandte(r) here.

haben comes with accusative.

Declension can change depending on the kind of your determiner/article. The negating article kein/keine requires the same declension as a definite article like der/die/das

So you could say the following things:

Ich habe Verwandte (plural without arcticle / indefinite article)

Ich mag die Verwandten (definite article)

Ich habe keine Verwandten / Ich mag keine Verwandten (keine requiring the definite article declension)

These examples are all accusative by the way, hope that helps

Verwandte is a noun as well as an adjective, so it declines like an adjective instead of a noun. The way I learned it was by copying down the information from the website below and just reading it over and over. It’s very easy to understand when you do it like this.

Here’s the website: https://easy-deutsch.de/en/adjectives/adjective-declension-easy/

I'm confused as well.

I don't know what your previous question was, but perhaps Verwandte did not have an article before it such as keine and so it had strong inflection rather than mixed or weak?

Sentences aren't in any case.

Parts of sentences are in a case, to show their role in the sentence.

In this sentence, sie is in the nominative case because it's the subject of haben and keine Verwandten is in the accusative case because it's the direct object of haben.

It inflects like an adjective, meaning that the ending will follow strong, weak, or mixed inflection depending on what is in front of it.

In your two sentences, you have mixed inflection after keine in the first sentence, and strong inflection in the second sentence since there is no article or other determiner in front of it.

Or to look at it differently, the -e ending for nominative plural is on keine in the first sentence (so Verwandt- doesn't have to show the case and can take the generic weak ending -en), but in the second sentence, there's nothing else to show the case and so the word Verwandt- has to have the -e ending for nominative plural.