I agree with Chosen's comments other than telling her to stay away from married men. When you're breaking up with someone, it's not really the time to be giving them advice unless it's the "You don't want to use that tazer honey, you'll just have to buy new leads and I'm not worth all that. Please put down the tazer," kind.
Honesty is the best policy here, and kindness. Sit her down away from her children and tell her how you feel. I've been in your situation, and I too hate hurting people, and nearly every time it has been the right choice to simply be open and honest.
Except for the one time. I tried honesty, she didn't accept it. I tried just telling her it was over, she didn't accept it. So I told her I was cheating on her with my ex-wife and she dumped me. I wasn't cheating, but it was all I could do... At that point, all I wanted was out and I knew there was nothing I could do to keep that bridge from being burned beyond repair to I told her the one thing I knew she couldn't handle.