President Franklin Roosevelt was the first to name a personal envoy to the Vatican in 1939.He paid for the lodging out of his pocket as he was wealthy (helped with the votes I'm sure).

The Vatican claimed immunity under a U.S. law, the Foreign Sovereign Immunities Act of 1976, that allows foreign states to avoid being sued in court.

1984 Pres. Reagan raised the US envoy to the Vatican to full ambassadorship: " United States will have full diplomatic relations with the Holy See for the first time since 1867."

In 1867: "On hearing a rumour that the Pope was going to forbid American Protestants to hold services within Rome's city walls - services which were already being clandestinely held in private homes - the US Congress passed a resolution in 1867 saying that no federal funds could be used to maintain a diplomatic mission in Rome."https://www.theguardian.com/theguardian/2013/jan/11/vatican-usa-diplomatic-relations-1984-archive

A 1994 lawsuit against Pope John Paul II (search), also filed in Texas, was dismissed after the U.S. government filed a similar motion. 2005: The U.S. Justice Department has told a Texas court that a lawsuit accusing Pope Benedict XVI (search) of conspiring to cover up the sexual molestation of three boys by a seminarian should be dismissed because the pontiff enjoys immunity as head of state of the Holy See.http://www.foxnews.com/story/2005/09/20/us-says-pope-immune-from-molestation-lawsuit.html

In the Oregon case, the Obama administration backed the Vatican and said the appeals court erred in ruling that a victim’s claim of sexual abuse by a priest falls within the exception to foreign sovereign immunity law. https://www.reuters.com/article/us-pope-abuse-usa/supreme-court-rejects-vatican-appeal-in-sex-abuse-case-idUSTRE65R3UB20100628

Trump appoints and the Vatican accepts an adulteress as Ambassador:

Trump's choice of Callista Gingrich to serve as U.S. Ambassador to the Holy See will require Senate confirmation. There is little sign of opposition to her nomination, but it is not without controversy. She carried on an affair with Newt Gingrich for several years while he was still married to another woman, and their relationship troubled many conservative Christians. https://www.npr.org/2017/05/20/529276806/callista-gingrich-nominated-as-ambassador-to-the-vatican