The sisters and Real Housewives of Beverly Hills costars not only learned to dive like Olympians for the Stars in Danger: The High Dive special – which airs on Wednesday (8 p.m. ET) on Fox – but they also mended their relationship, which they thought had no chance of being saved.
"My sister and I had kind of a rough patch over the last couple of years and I thought [High Dive] would be a nice opportunity for Kyle and I to really bond," Kim, 48, told PEOPLE on Wednesday in Pasadena, Calif., during the Television Critics Association's winter tour. "It took us actually a step beyond closer. We're probably the closest we've maybe ever been ... I really didn't see any light at the end of the tunnel."
Kyle, 43, agrees it was participating challenging show that allowed her to see a different side of her sister, who completed rehab a year ago.
"The first day I had to get on the diving board, I was completely overcome by fear," Kyle explains. "I felt like I was going to faint. I couldn't feel my legs ... My sister felt very protective of me and kind of went into mama-bear mode ... We really had to support each other and I think that's the best thing that's come out of this for us. Kim and I are definitely in the best place we've been since we were little girls."
Adds the reality star with a laugh, "We've gotten over our rough patch, but I'm still afraid of heights."