General Hospital Week of June 2 Update: Brennan Under Pressure – Dalton Bonds – Paternity Cover-Up Crumbles

General Hospital (GH) spoilers update for the week of June 2-6 reveals that Professor Henry “Hank” Dalton (Daniel Goddard) and Jordan Ashford (Tanisha Harper) will bond while Jack Brennan (Chris McKenna) is under pressure. Carly Spencer (Laura Wright) will also get a shock, so there’ll be a lot going on in Port Charles.

For starters, Alexis Davis (Nancy Lee Grahn) will get grilled over the $10 million that’s been taken out of Ace Cassadine’s (Jay and Joey Clay) estate, so she’ll have to make excuses to Laura Collins (Genie Francis).

As for Lucky Spencer (Jonathan Jackson), it looks like he may come clean to Elizabeth Baldwin (Rebecca Herbst) about Kristina Corinthos-Davis’ (Kate Mansi) role in the crash.

Lucky will also have to face a difficult truth later, so he may start to accept that maybe he’s not meant to settle down.

Is the show on the verge of sending Lucky back off canvas?

Next, Brook Lynn Quartermaine (Amanda Setton) will rip into Gloria Cerullo (Ellen Travolta) for helping Lois Cerullo (Rena Sofer) cover up Giovanni “Gio” Palmeri’s (Giovanni Mazza) true identity all these years.

Afterward, Brook Lynn will have a heated confrontation with Lulu Spencer (Alexa Havins Bruening) for blowing up the secret and devastating Gio in the process.

Once Sonny swears he was in the dark on being Gio’s grandfather, he’ll offer some words of wisdom.

Sonny will also have a chance to confide in Jason Morgan (Steve Burton) about Gio, Michael Corinthos (Rory Gibson) and anything else on his mind.

Michael and Willow Corinthos’ (Katelyn MacMullen) custody battle will move forward, so that’ll bring an opportunity for some wild courtroom moments.

It looks like the paternity of Sasha Corbin’s (Sofia Mattsson) baby will be exposed and unleash some chaos.

GH spoilers say Willow’s going to leap into action eventually, so she may take advantage of the upper hand that Ric Lansing (Rick Hearst) potentially gets for her.

Nina Reeves (Cynthia Watros) will ultimately have an admission to make.

Will Nina tell Willow that she supplied the paternity shocker to Ric – or could this finally be a confession about her hookups with Drew?

Whatever the case, Drew will end up troubled by the end of the week.

However, that could be more about Curtis Ashford (Donnell Turner) and Portia Robinson (Brook Kerr) finding Jacinda (Paige Herschell) since they intend to use her to neutralize Drew.

Portia and Curtis will also host a family party, so we’ll see if Trina Robinson (Tabyana Ali) might bring Kai Taylor (Jens Austin Astrup) to the get-together.

Jordan has a meeting with Curtis coming up, but she’ll get better acquainted with Professor Dalton first.

Shady Professor Dalton has plenty of things to hide, so will Jordan pick up on any strange hints during their possibly flirty discussion?

Back with Jason, he’ll face Carly’s questions once she deals with the paternity shock.

Jason has been posing as Sasha’s baby daddy, so Carly won’t like that she’s just now hearing about this.

Over with Brennan, he’ll end up under pressure.

Anna Devane (Finola Hughes) will put Brennan on the spot and try to pry info out of him, so she’ll give Jason updates on her suspicions later.

General Hospital spoilers say Anna will have a theory she’s working on, so stay tuned to see if this involves news on Sonny’s mysterious foe.