In this week's PEOPLE cover story, the country singer, 58, makes clear that "there is no argument" between her and the actress, 54, over their late mom Naomi's will.
"Someone told me while I was at Ashley's house, 'Hey, did you know that they're saying this about you?' I went, 'Huh? I'm fighting with Ashley? Oh. Again?'" Wynonna recalls. "Fighting over what? I have such a great life. Ashley has a great life. Why would we be fighting over the will?"
Wynonna says Naomi — who died by suicide in April at age 76 — appointed her husband of 33 years, Larry Strickland, as the executor of her estate prior to her death. When he dies, Wynonna says she and Ashley will then "split" the estate, and she has no plans to contest the will.
"I am the last person in this family — and if Ashley was here, I'd hope she'd agree with me — who knows stuff like this," she says. "I'm not savvy enough to go, 'I'm going to contest the will.' It never occurred to me."
Jim Wright Wynonna Judd
Since their mother's death, Wynonna (whose father is Charles Jordan) says she and Ashley (whose father is Michael Cimenella) have only been brought closer together.
"I feel like we're connected in a way that is so different because I'm an orphan," she says. "Both my parents are gone, and I'm relying on Ashley. She's relying on me in a different way that's about compassion. It's not about being successful and smart and capable. It's about, 'I love you.' 'I love you, too.' We're vulnerable with each other, and we're tender."
"As sisters, we disagree on so much," she adds. "But when it comes to our mother, we both look at each other and go, 'She was quite the character.'"
RELATED: Wynonna Judd on Mom Naomi: 'With the Same Determination She Had to Live, She Was Determined to Die'
Ke.Mazur/WireImage Ashley Judd, Naomi Judd and Wynonna Judd
It's been a long road for the sisters, whose relationship has been fraught with disagreements through the years. In 2012, neither Ashley nor Naomi were in attendance at Wynonna's low-key wedding to husband Cactus Moser.
"[Ashley and I] were separated at age 14 and 18 by success," Wynonna says. "So we've missed out on a lot of time together."
Watch the full episode of People Cover Story: Wynonna Judd below or on the PeopleTV app.
With help from a life coach, Wynonna — who kicked off The Judds: The Final Tour on Sept. 30 — says she and Ashley were able to get to a better place.
"Ashley and I are very different people, and we are learning that we have more in common than we don't," she says. "That's really interesting, because when you're younger, you think there's more disconnect. We had a really deep conversation the other day, and we got through it and nobody got hurt."
Jim Wright Wynonna Judd on the cover of PEOPLE
"We've been able to work the process our life coach has given us: communication, compromise and compassion," she continues. "In my disagreements with Ashley and Mom, I never gave up loving them, because I knew behind all that, there was someplace to meet and connect upon. I tell people: Try to find something that you have in common. Ashley and I, when it all goes to hell, can play cards and get along."
At the end of the day, "the best revenge is living well," Wynonna says, "and the relationship I have with my sister is the most powerful in my life."
Jim Wright Wynonna Judd
For all the details on Wynonna Judd's journey through grief, pick up the latest issue of PEOPLE, on newsstands everywhere Friday.
If you or someone you know is considering suicide, please contact the 988 Suicide and Crisis Lifeline by dialing 988, text "STRENGTH" to the Crisis Text Line at 741741 or go to 988lifeline.org.
If you or someone you know needs mental health help, text "STRENGTH" to the Crisis Text Line at 741-741 to be connected to a certified crisis counselor.