Everyone has a "dating score", it's like a credit score, but more subtle.
Let's get real, these days, men get VERY little benefit from a relationship with a woman. That's not some "anti-feminist, anti-woman" thing, it's reality. As women, we are not shy in telling the world how great we are, how much we deserve, how we won't date any man who isn't earning 100k, has his own place, wants kids etc. BUT, we don't seem to accept that men also have their own standards. If we don't want a man, for whatever reason, we say "he doesn't deserve me", "he's a loser", "he's not good enough to be with me".
Well, man do the same with us, and most of us have NOTHING to offer except an over-inflated sense of self-importance, a pair of "love island lips" and a bitchy attitude. And those are just the women without kids.
In reality, single men, who aren't fathers, have ZERO interest in a LTR with a woman who has kids. And even less desire to be with a someone who says things like "I dont need a man", because men want to be needed, they are driven to be providers and protectors, and if the first thing you say is "I dont need you to provide anything, or offer an protection" then why should they be with you?
In respect of being a "single mother", all things considered, those kids are about THE worst thing you can have on your "dating file". It's like asking a bank for a loan when you can't afford the repayments. So, that leaves you with the men who already have kids. And in 99% of those cases, there will be a "psycho ex" or whatever term the guy will put on the woman who he views as having taken his kids and home away from him. For those men, a LTR is the last thing they are going to want. A quick shag maybe, but they have no interest in playing second fiddle to a five year old.
Much as we might want to view ourselves as the smoking hot, alpha female, that men just can't resist. Men just don't see us like that.
So yes, it will be significantly harder for you to find a man who wants to "take on" you and your kids. That's not misogyny, it's reality. Forget men who don't already have kids, you've already see how that just doesn't work. If you can't wait until your kids are adults (which is what I would recommend) then find a guy with kids, at least they understand something of the reality of taking care of them.
But you need to drop the "I don't need a man" attitude, from my guy friends, thats THE biggest turn off for guys.