Did Frank Sinatra pay for her body to be returned to the U.S. and the funeral expenses there?

No, Frank did not pay for any of the expenses related to Ava's return to Smithfield or her burial. Contrary to rumors, he also did not pay her medical expenses after her stroke or before her death. They remained very close friends, however, and he was in touch with her on a regular basis during the last years of her life.

I would call directly and ask the docent.

I didnt see anything on that. If you can't get a definitive answer on the Web (like Wiki), or want confirmation, I'm sure one of the curators there would be glad to help you. Just call.