Like any parent, Elliot talked about his children all the time. A case involving children would affect Elliot close to home and while Olivia wasn't a parent, she sometimes understood his point of view the best she could.
In the first season, Olivia and the Stabler children did not share any scenes (although they may have met off-screen) until the second season in a brief scene.
After Dickie was recovering from appencidis, Olivia asked in concern about him and if Elliot and Kathy ever wondered what their kids would be as grown ups. At least Elliot and Kathy knew what they're passing to their kids while Olivia's DNA was drunk and cruel.
There was a momentary worry for Elliot when he realized from the HIV patients list that Kathleen's ex-boyfriend was on it. But Kathleen never slept with him. However, Kathleen started to have her own problems with the law, starting with getting a DUI.
In the seventh season, the children did not appear during the entire season. However, there were a few references. Elliot was still having a tough time with the separation, which progressed into divorce proceedings. He was also reeling from missing his children and refusing to go home. Elliot spent most nights sleeping in the crib at work.
In the eigth season, Olivia could see the fatherly pride in Elliot's face when Kathy called him about Dickie's suspension for punching a kid. After discovering three children and a wife dead, Elliot was shaken up that he needed to leave. Olivia went to update Don while Elliot went to see his wife and children. A few months later, Olivia was the first person Elliot told that Kathy was pregnant. Olivia was surprised as Elliot hadn't moved back home yet and asked what he was going to do? Elliot didn't know what she meant by that, but they were interrupted before Olivia could answer.
By the time Kathy was nearing the end of her pregnancy, she had an appointment with her OB/GYN and needed a ride as her car was in the shop. Elliot was planning to do that but forgot about it after finding a body of a woman involved in their case. Elliot went to North Forks which was 3 hours away so Olivia volunteered to take Kathy to the appointment. While on their way, a drunk driver slammed into Olivia's car on the passenger (Kathy) side. Kathy's legs were pinned under the dashboard, she was dehydrated and in labor. The firefighters managed to get Kathy out of the car and into the ambulance where she gave birth to a baby boy. Olivia helped coach Kathy and was happy until she realized Kathy wasn't responding. Kathy needed more fluids and her heart briefly stopped; meanwhile Olivia took the baby, keeping him warm with a thermal blanket while paramedics worked on Kathy. At the hospital, Elliot rushed past Olivia to Kathy's room. After the visit, Olivia was waiting outside the room when Elliot came out. He hugged Olivia as a Thank You. Olivia asked if they picked a name- Kathy wanted to name the baby after Elliot. Just want the world needs: another Elliot Stabler.
At one point, Elliot was concern for Olivia over the stolen embryos case for being over 40, using Kathy as an example but Eli was a healthy baby.
Kathleen got into more trouble after stealing her father's credit card and then she broke into a home, stealing an antique necklace and taking a shower. Olivia took the case and learned from Kathy that Elliot's mother (who she didn't know about) had the same condition as Kathleen. Olivia took Bernie to see Kathleen in jail. Kathleen admitted to the court that she's sick and will take the medication with Olivia in the room, sitting next to Kathy.
Olivia was given guardianship of a premature baby girl, who's health was threatened. She asked Elliot what he would've done if Eli was sick and there was nothing he could do- Elliot isn't God.
In the twelvth season, Olivia was to speak at Take Back the Night rally for rape victims for Kathleen at her college. But her guardian child, Calvin Arliss, was having a tummy ache. A rape victim came forward, accusing Chuck Mills of rape, which Olivia got involved in.
Months later, Olivia got the news that Elliot was being accused of molestation in court and went to tell him; Elliot saw her coming, telling her that he needed to take an hour lunch to meet with a preschool for Eli until he realized something was up.