05/27/2010 at 01:20 PM EDT
It has been one year since the marriage of Kate and Jon Gosselin began to crumble
in plain view – and Kate
acknowledges there have been difficult moments for their brood of eight.
"[Nine-year-old daughter Cara] was upset with me because I forgot to sign them up for something at school," Kate, 35, tells PEOPLE in a new cover story. "I said, 'Cara, I had a really rough year. This is a new year. You've got to give me that. Let's start over.' So I've really worked to keep my word with them."
In general, Kate says, her children – twins Cara and Mady and sextuplets Alexis, Hannah, Leah, Aaden, Collin and Joel – have weathered the storm well: "They're just amazing, resilient, loving kids."
The reality TV mom and her kids will return to TLC in a new special, Kate Plus 8
, airing June 6. The family recently filmed the special in Orlando, Fla., where they also celebrated the sextuplets' sixth birthday.
For more on Kate and the Gosselin kids, pick up the new issue of PEOPLE, on newsstands Friday