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"I'm tired of people thinking that my boyfriend's a bad father, especially now that I'm having his baby," Oglesby, 20, reveals. "He's an awesome dad."
Johnston, who released a tell-all memoir Deer in the Headlights: My Life in Sarah Palin's Crosshairs last fall, claims his son's maternal family has kept him from having adequate access to his son.
"I love Tripp more than anything and he is my son, but I don't feel like a dad to him," the Alaskan native shares. "But it is what it is, and maybe one day I can be."
Oglesby and Johnston say they would "love" for Tripp to be a bigger part of their lives after their baby is born so he can get to know his younger sibling. But Johnston admits he thinks Bristol's family -- especially her mother, former Alaska governor Sarah Palin -- plays "a big role" in restricting his access to Tripp.
"That's a family," Johnston tells host Brook Anderson. "I know I listen to my family, so I'm sure [Sarah] does have some part in [keeping Tripp away]."
But the Palins say Johnston's accusations are a lie. In a statement to TMZ, Sarah and Todd Palin denied that they've ever tried to keep their grandson away from their daughter's ex.
"We have never hidden Tripp from Levi or discouraged Levi from spending time with him," the pair wrote. "Any suggestion that we have is false and contrary to our core beliefs."