The show has successfully kept people guessing about Brenda's baby, despite how unpopular the story is. Who's the father? Where's the baby? Etc. Here's my theory.
We know that Dante was infatuated with Brenda when he guarded her in 2007. We do not know for a fact that the relationship was more than friendship. In all the flashbacks that Brenda & Dante have had, not once has there been a flashback to lovemaking. That to me is the most obvious clue that the "relationship" was like the one Brenda & Jason have, minus the humor. He was her Jason substitute.
As to her pregnancy & him signing away legal rights to the child, I believe Brenda dated Alexander, knowing what his family was involved in, until she got pregnant. She left him because she was pregnant & spilled her guts to Dante about all of it. They decided to mislead the Balkan into thinking that she left Alexander for Dante & got pregnant after she was no longer with Alexander. The legal document was part of a paper trail confirming it.
As for the baby, I don't believe Brenda carried to term. Ironically, I think the Balkan killed his own grandson one of the times he attempted to kill/disfigure Brenda. I think that is the reason she does not want to talk about the baby. That actually plays honestly into the character's history & how she's always dealt with difficult things.
If this is where the writers are going, they may yet hit this one out of the park. Especially, with Carly thinking she has something special with her "proof". But, that leads into my next complaint...
Why exactly is this baby secret a ticking bomb? Even if it is Dante's, where's the problem? Surely no one, esp. Sonny has forgotten that he slept with both mother (Alexis) & daughter (Sam) & he had both affairs while he was married & both produced children.
My other problem is this...Yes, Carly hates both Brenda & Dante & wants them both to suffer, but since when did she become someone who wants children to suffer? She knows Brenda has a lunatic child trafficer after her, didn't it occur to her (or at least to Diane or supposed genius Spinelli), that the Balkan might decide a fitting punishment for Brenda & Dante would be to kill their child? A child which is Sonny's grandchild & Michael, Morgan & Kristina's niece or nephew? How does she think Sonny will show his gratitude for her getting his only grandchild killed? Carly used to be smart enough to see these things ahead of time. Another case of dumbing down a character for a five minute shock & awe moment.
Just once, I'd like for Sonny (who, we're constantly told is so intelligent), to be one step ahead & already know all about Brenda & Dante's "history" from when he looked into her past before he went to Rome. He could simply be waiting for her to tell him when she's ready & it would go a long way toward bringing back the Sonny we used to like.