The answer to your question would be that the sentence that is written correctly is the following one: Milo's puppies are still with their mother.
The sentence in question is an example of subject verb agreement. Subject verb agreement means that the subject and the verb must agree in number. In other words, both of them should be either singular or plural. In this case, the NP "Milo's puppies" is the subject of the sentence. The head of this NP is "puppies", which is a plural noun. Therefore, the verb must also be plural (are).
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