Hayden was indeed involved with Nikolas. After the debacle with her pretending to be Jake Doe's long-lost wife, Nikolas discovered her real identity (the daughter of a disgraced financier/ponzi schemer) and blackmailed her. Things went south, however, when she tried to double-cross him or something (fuzzy memory), so he casually hired a hitman to kill her. She was shot in the head and went into a coma. We thought that would be the last we'd see of Rebecca Budig, but they decided to wake Hayden back up and have her pretend to have amnesia. Nik pulled her close to keep an eye on her, then they sort of fell in love...but Nik ended up (presumed) dead, and she of course moved on to Finn and was revealed to be Liz's sister.
I'm guessing she is back in town as part of Nikolas's return, like maybe he looked her up while she was in Europe and enlisted her help in bringing down Valentin. Not sure why Jax would be along for the ride, but maybe they just haven't revealed that part yet. If Nikolas is supposed to be returning as a sort of anti-hero, maybe she's back in love with him again. If they're going full-blown Cassadine with him and turning him into a villain, then he might have her baby as a hostage while she does his bidding. The "unidentified man" seen with Cassandra Pierce might be a plastic-surgeried Nikolas, and she might have a history with Jax that motivates him to join in on a plot to catch her. Since Finn is the father of Hayden's baby (and Cassandra hates Finn with a passion), that might factor into the plotline, as well. I'm hoping Anna will be involved when Finola Hughes returns from summer vacation, as well.
One thing I keep hearing, however, is that RB is only back for a four-month arc, so whatever the plotline, she won't be sticking around after it gets finished.