You have a couple of problems and they should be separated so you can deal with each of them individually.
First of all, you're in a loveless or a troubled relationship. You feel like the love is gone - and maybe it is. Thirteen years and 2 kids, and you're settled into the boring and mundane part of life. But you aren't committed enough to get married - which is fine, if this isn't the guy for you. But you aren't dealing with it. You're drifting along, calling him your "fiancé" but unwilling to either get married or break up. So deal with that first. You are absolutely right that you don't stay with someone to make your kids happy. The best thing you can do for them is get your life straightened out. No matter whether you stay with their father or not, you have to co-parent with him at least until the kids are 18 and maybe beyond if there is college to deal with. So, get counseling.
Second problem: you met someone on line, and you're doing the young love/giddy/joyful love thing. That's a great feeling, Isn't it? But here's the thing: you don't know this person at all! You're both caught up in the lovey-dovey stuff with none of the commitment or work of a relationship! You've in the infatuation stage - it was fun and exciting and maybe just a little bit of that was because it's a secret. But it's based solely on attraction and maybe on your understandable need to be thought of as attractive and desirable and fascinating. That's important to feel - but it's not based on any depth. Maybe there's a future in this, and maybe there isn't.
You have 2 kids. They're yours no matter what. You need to end the relationship with their father if that's your plan, and take very good care of them during the process. That means getting counseling, at least for you and probably for your fiancé, and possibly for the older child too (and at least you need to work on how to explain this to the little one). You need to get finances, insurance, assets, possessions and living arrangements in order.
When that is done - and ONLY when that is done - and after you have a good period of separation, then you can consider a new relationship. But first you have to find yourself and figure out who you are. You cannot give yourself to another person until you get her figured out! But you do not - absolutely DO NOT - introduce this person to your children!
Now, you have met someone and your entire "relationship" is on line or maybe at lunch or whatever. You have stated your love to someone who is willing to "fall in love" with someone on line. You have no idea if he has done this before or if he has other "relationships" like this going on at the same time. I'm not trying to say he's a bad person. I'm saying, you have no idea. And if neither one of you is being sensible, so that's a huge problem. And the fact that you both have talked about merging your families without even knowing if there's a future to this relationship says that you are both dreamers and not practical people. You two don't even know if you can stand the way the other chews or laughs too loud at movies, let alone whether you are compatible.
Please get rid of the idea that you "met for a reason" - that's a dodge, to put the decisions about a relationship on "the universe" or on "fate" rather than squarely in the hands of the two people responsible for running it.
Look, my husband and I were attracted to each other after months of being office colleagues. We met for lunch and discussed our attraction. So I'm judging you for meeting up with someone - I did it too. I was single but healing from a not-well-handled break-up many months back, and he was still married although very unhappily (she was out all night while he was home with the 2 kids). So, what we did was, he talked to her about separating, and he moved out. He got counseling (he had been doing it all along anyway, but he focused on the separation and what the kids needed). After he was single (although the divorce took a while to be final), we started dating. We did not sleep together or talk about long range plans. We got to know each other first - and in person, not on line! I did not meet his children for a very long time. We didn't say we loved each other, and he didn't use me as a soft place to fall. He saw himself, and his children saw him, as a single man long before they saw him in a relationship with another woman. We are happily married for over 30 years - probably because we did this right.
So, your infatuation with this man has highlighted the many shortcomings in your relationship with your fiancé. That's a good thing, as long as you use it for constructive analysis (with professional help) of your family life. But you have to put your children ahead of this man, and you have to successfully end the current relationship before you put yourself into a new relationship. Just because the spark is gone from your relationship doesn't mean that you just "change the batteries" and everything is recharged! If you cannot see yourself as a single, independent, strong woman, then you are not ready to get into a relationship with another man. The way you are doing it has "disaster" written all over it.
So, call a counselor, talk this through, and then figure out what you're going to say to your fiancé, either alone or in couples counseling. And put the other man on ice for the moment, telling him you have to get your ducks in a row on the home front no matter how exhilarating you find the "forbidden love." If there's a future here, he will work on his situation with a counselor to talk about integrating any possible new people into his children's lives, while you talk about it on your end.
But you cannot leave one man for another, or you will have 2 failed relationships on your resume.