The zoo does indeed have three elephants: Happy, Patty, and Maxine. Patty and Maxine live together and Happy lives alone as she does not get along with the other elephants. All previous attempts to properly mix her with the other two have resulted in fights, including one in 2002 where her previous companion, Grumpy, ended up sustaining injuries which killed her. The zoo had looked into sending her away once, but concluded that, after over 30 years of living at the zoo, a move would likely be too stressful for her. As mentioned, Happy is thoroughly enriched by her keepers, many of whom she is well acquainted with and she also gets limited interaction with Patty and Maxine through fences and such. The zoo alternates which elephant(s) is/are on-exhibit (Patty and Maxine are exhibited the most) but also have several off-exhibit yards for whichever animal(s) isn't/aren't.
The zoo has been facing lawsuits and criticism over Happy for a long time now. PeTA has called for the AZA to strip the zoo of their accreditation, there have been many online petitions (some 200,000 supporters strong) against the zoo, and In Defense of Animals has featured the zoo on their 'Ten Worst Zoos for Elephants' lists every year since 2012, as well as listing it in 2009. Of course there was also the infamous 2012 New York Post article I mentioned earlier where some asshat "journalist" made up a story that the zoo locked her indoors year-round and kept her in solitary confinement. The contents of this article have been the main arguments against the zoo in most of the petitions and movements regarding Happy.
~Thylo