What is wrong with the construction "Он отдыхает сейчас?"
Adverbs normally come before the verb in Russian
"Having a rest" is just very unnatural -- not something we would ever say in English, or at least not in America.
Why doesn't "having" signal the "у ему" construction. "Она сейчас отдыхает" seems like it should translate to "he is resting now".