Of course, being an imbecile propelled by the belief that everyone wants to destroy her because they hate her is not the only thing Connie can exploit. Elly's love for stupid solutions also comes into play. As by way of example, let's remind ourselves of what happened when Elly finally figured out how April was able to defeat the latch to that back gate. Simply put, Tweedle-Dee The Wonder Dummy forgot that April was three and didn't tell her "Ask Mommy or Daddy or Mommy's Friend Girl Skeletor if you can leave the yard." Anyone with two clues to rub together would see that that would be a problem.
Sadly, Elly hasn't got two clues and can't see warning signs that are glaringly obvious. She can be told time and again that there's something that she needs to pay attention to but since she's a lazy woman and since that would get in the way of doing what she wants to do, simply blows off said unfair advice until it's too damned late. Worse still, she doesn't see the obvious when it's staring her in the face and when the worse happens, comes to a ridiculous conclusion.
This tells me that it was easy peasy for Connie to allude to the fact that Annie just plain forgave Steve because Elly's stupid enough to believe it, paranoid enough for that to fit her preconceptions that everyone is trying to keep women down, lazy enough not to check and crazy enough to draw an irrational conclusion from the unvarnished truth. All she needed to do was made an imbecile think that she's smart.