My advice is coming from my experience as a child whos parents divorced when I was 10. My parents set me down and discussed that they were divorcing and before they divorced my Dad had a "work partner" who he just brought home one day and more and more she'd appear at our home. Eventually she lived with us and then they married.
Personally, I wish they would have kept their dating matters quiet and just concentrated their time on me. I should not have met my Moms boyfriend or my Dads girlfriend.
I remember the first time I met my Moms boyfriend and I was angry that my Mom left the vehicle to spend time with him.
Kids go through enough with divorce and not seeing their parents together and to complicate things by dating is worse for them in my opinion.
Raise them until 18 and then introduce them. That way you'll be ready to marry and your kids would be fully raised.
If you are bound and determined to still expose them to your dating partner then I would ask them what they think if you started dating again. If they do not like it then don't expose them. I'm sure you want to be happy and in doing so you'll want to date so maybe you'll want to date in secret so you don't hurt your kids. Ask them every 6 months or so about how they feel if you were to date and once they are accepting of it then wait a month or so and ask them to join you for dinner with a friend. Just you, your boyfriend, and your kids. Maybe expose your kids to his kids later. You don't want to overwhelm them. Over a period of time that "friend" can come around more and more. You can go on dates here and there with your kids. Maybe your kids will start asking questions and then you can tell them about his kids and see if you all want to go on a play date or something.
It's very hard for you and it's hard for the kids involved.