"With her, his actions will have to speak louder than words," Bristol, 19, tells PEOPLE. "And he'll have to get his education and a job and be willing to support Tripp the right way. And then I think she'll come around."
What does she mean by "the right way" to raise their 18-month-old son?
"Like, not just have him around when the cameras are around but be there all the time and have a legitimate job and be supportive financially and just set a good example for him," says Bristol.
According to Bristol, Johnston is really changing. "Tons and tons of progress is being made," she says. "Like, he'll change a diaper without me even having to tell him, or he'll take him when I need a 15-minute break, or he'll come over and help with Tripp, and all that stuff is just so much appreciated."
Sarah Palin, 46, who is currently hiking Mount McKinley with her family, issued a statement, saying, "Bristol, at 19, is now a young adult. As parents we obviously want what is best for our children, but Bristol is ultimately in charge of determining what is best for her and her beautiful son. Bristol believes in redemption and forgiveness to a degree most of us struggle to put in practice in our daily lives. We pray that, as a couple, Bristol and Levi’s relationship matures into one that will allow Tripp to grow up graced with two loving parents in his life."
Earlier this month, Johnston, 20, publicly apologized to the Palin family for saying things "that were not completely true" following his and Bristol's breakup last year. He blamed his remarks on "youthful indiscretion."
"I hope one day to restore your trust," he added.
While that apology was also offered in person, Johnston has not spent any more private time with Sarah.
"There has not been anything where all three of us [have been together]," says Bristol. "I see the future like that being possible, where we can all have Thanksgiving together and not have it be awkward. But his actions need to speak louder than words."