Is the middle section of this sentence an appositive?

Solution 1:

It depends on the speaker's intention.

If the speaker's intention is to simply rephrase the word "custody," then it is. It's an appositive because what follows is just a renaming of the word "custody."

If the speaker's intention is to specify how they mean "custody," say to contrast it from a legal definition that means the person is under arrest, then it's not. In this situation, it's modifying "custody" to explain which "custody" is being referring to, i.e., a lay one and not a legal one. It's not an appositive because what follows isn't just a renaming of the word "custody" as it restrictively describes which of any number of versions of the word is being used.