(CNN) -- Kate Gosselin last appeared on Larry King Live on May 10. A little more than a month later, on June 22, she and her husband Jon filed for divorce and announced their split that same day in a special edition of their show.
Kate Gosselin says she and her kids would like to continue their TV show, but admits it will be up to the network.
Gosselin returned to Larry King Live on Tuesday to discuss her sextuplets, the future of her show and how she feels about Jon.
The following is an edited version of the interview:
Larry King: How much do they know about what's going on? The 9-year-olds probably do, right?
Kate Gosselin: They understand the process. They're working through it, the same that Jon and I are. They're doing remarkably well. This has opened up a lot of discussions between them and myself. A lot of questions come my way, and we're dealing with it. They're doing very well considering. Watch Gosselin discuss the split »
King: Why did you agree to do this reality show in the first place?
Gosselin: In the very beginning, we started filming a one-hour special. It was a way to document what was happening in our lives. At that time, there was a lot of local news stories. There were a lot of people in the country and the world, believe it or not, pulling for us. As you know, sextuplets are not born every day, so there was a lot of interest.
We did the one-hour special to show everyone. I always pictured like the little old lady that was sitting at home who was praying for us, rooting for us and needing to know what happened to those babies that were born. So we did it for that reason as well as to collect the memories for ourselves.
King: Why did you agree to do a regular reality show? You could have said that's the special, here's my life, goodbye.
Gosselin: I could have. At that point, the one-hour special was a very good experience. The network, TLC, we were on Discovery Health at that time. Now, TLC is wonderful, supportive, and it was a great experience for us. So we, you know, really moved forward because of that reason. It was healthy and safe and fun.
King: Do the kids talk to you about divorce?
Gosselin: They do. And as any child, you know, when their parents are divorcing, the goal is peace and we've achieved that numerous times. The Fourth of July we spent together as a family. My goal is, no matter what the circumstance, no matter what place, you know, one of us is in, my goal is really peace and the best that it can be for the kids.
King: Do they get counseling?
Gosselin: We have not started that process, but I feel like it is a very normal thing to do. And absolutely, when the time is right.
King: Jon is quoted in the new "Us Weekly": "I wish I had a 9 to 5 job instead of the nightmare I'm living. This is 24/7. I don't even want to do taping the show anymore." What's your reaction to that?
Gosselin: Jon's opinions and his goals are his. I know that, personally, for myself and the kids, this has been a good experience. It continues to be a good experience. And, you know, really the network has been extremely supportive, above and beyond, I feel, what they need to be. And I only experience good things.
Everyone works. Everyone has a job. Everyone has what they're dealing with. And, generally speaking, this is the most flexible, workable, wonderful job for myself.
King: How long have you been doing it now?
Gosselin: We are in season 5. We started filming in August of 2005.
King: Why is it such a good thing to have a private life public?
Gosselin: It's been a source of huge -- for whatever reason -- inspiration for a lot of people. Many, many people -- many parents feel that their decisions are, maybe not, great decisions. Every parent has that, you know, parent guilt of my goal is to produce wonderful, productive individuals and put them out into society. That is the goal of a parent -- for us to show the world that we are not perfect, life is unpredictable, but life always goes on and there's always, always, always something to look forward to. And for me, that is raising my children to the best of my ability.
King: But as an intelligent person, you also know to all good things, there are downsides.
Gosselin: Absolutely. With every positive, there is a negative across the board in life. It's about choosing to see the positive and working with the negative.
King: So what happens now? Are you and the kids going to do the show and Jon is out?
Gosselin: I'm not the person to make that decision. I know that myself and the kids will continue the show.
King: But if Jon says I don't want to do it anymore, I don't want to be part of it, I'm divorced, I don't need this, will the network say it's you and the kids?
Gosselin: That would be a question for the network.
King: Will the name of the show change?
Gosselin: That would be a question for the network.
King: And if they said forget it, that would be OK with you? If they said we'll continue, that's OK with you?
Gosselin: That will be their decision.
King: You've become famous worldwide over this. What's the downside of that?
Gosselin: You know, I could really live without the following.
Gosselin: Yes. I could live my whole life -- I would have to say that is absolutely the negative. I realize it comes with it. I know that it goes along with it. I'm smart enough to figure out that, you know, there's interest. It's going to be interest across the board. It's another learning lesson.
King: You and Jon renewed your marriage vows a year ago this month in Hawaii. What happened? How do you go from renewing vows to filing for divorce in a year?
Gosselin: It is a question I ask myself every day. I don't have the answer.
King: But (Jon) made this decision?
Gosselin: You know, it's just an issue that we discussed amongst ourselves. I don't feel like that is something that we need to discuss the details of.
King: Yes, but when you get so famous, you and him and the kids, and then you leave out those details, don't you disappoint the audience that's come to expect more?
Gosselin: My main concern is my kids. And I don't want them to see or hear anything on TV that I didn't discuss with them. And we discussed what they need to know at their developmental age groups. But I don't feel like I need to go any further than that at this time.