I was in a similar situation, except I only had 1 child. I discovered later in the marriage that he was volatile and suffered from mental illness, had a bad credit history, and on occasion, he'd also be under the influence of drugs. We constantly argued and I was always crying and miserable. Like you, I did not feel love. I even tried strong anti-depression medication to end my suffering, but I still felt dead inside.
Everyone kept telling me to stop being selfish and put my child first, even if it meant staying in an unhappy marriage. I tried that twice, and both times, I realized I was unhappy and my daughter perceived that. Maybe those people mean well, but I don't think it's a good idea to stay in a marriage in which your stress levels are always sky-rocketing. Don't judge unless you've been there, I'd say, and the funny thing is, some of these women were in abusive relationships with addicts, and they still said staying is the only way. I totally disagree.
I grew up with parents who constantly argued and it suddenly dawned on me how much I hated it, how nervous I'd get every time I'd hear doors slam, and how even now, loud noises and banging makes me jumpy. At that point, I realized it wasn't just about ME, it was also about my kid. I did not want her to grow up listening to shouting match arguments like I did. When she told me once to please stop arguing with him with tears in her eyes, I knew that I was done trying. He was coming home at 3-4 a.m., in case you're wondering why we'd argue at times. Unlike you though, I was also financially supporting him. I was always budgeting, he was always spending all the money he had and in debt.
I have been alone for many years. I tried dating during that time, though I never sought men, I'd just meet them at a museum tour or what have you, but I could not find anyone mature enough to want to try a relationship, so I gave up on that. Never during that time would I introduce these people to my child. My self-imposed rule was that we'd have to date at least 6 months before that happened, but I never made it to that point. I am comfortable and okay with thing as they are. I am very much at peace with myself, my stress levels have gone down, I am a happier person all around, and love having time for myself at home to read or catch up on a movie. My daughter loves spending time snuggling on the couch watching a movie, just the 2 of us. Finding love, as you can see, is not my priority nor does it matter. I hope that your main priority isn't finding love because some people never even find it in their lifetime, so you have to be prepared for that. In the meantime, you can always have great friends you click with, laugh with, and feel that connection that you feel you lack.
Is it easy being a single mom? Heck no, you're expected to be both mom AND dad and have the same amount of time to do homework, cook, etc., as a two-parent household that splits the chores. It won't be easy. Some people will judge you, including a lot of men that may avoid you like the plague because of a stereotype that if you're a single mom, you must be looking for a sugar daddy to support you and your kids. You are responsible for more than one person financially, so that is a lot of burden to carry because if you lose your job, no one is going to assist you, so you have to be very responsible at your job.
You mentioned you're unable to support yourself. An option you may want to look into is trying to find someone who is renting an apartment and is seeking a roommate. Try craigslist. There are responsible women out there who have a lease, but may feel lonely and want a roommate, or they need help with paying the rent/mortgage, and they want to find someone responsible and mature that won't try to gyp them. Some of them are college grads in grad school, and some may be single moms. Who knows, if you find a single mom, your kids might like playing with her kids. I have seen apartments that look clean and in good areas where the person looking for a a roommate asks as little as $600 a month in rent. I don't know if you work or not, so I don't know if that's even feasible.
All you can do is think this through and take into account that perhaps you may not find Mr. Right, and if you still feel that you want to end things, do it now before it's too late. After 18 years, I feel it will affect everyone even more that you carried a lie for so long and suddenly dropped a huge bomb. I don't think it is wise to do this, although everyone may have a different opinion on that. Realize that your kids may be upset that they lived a lie for so long, or feel they grew up not seeing love because you two thought prolonging the inevitable would be the best option.