This is where you're going wrong.
I have a theory that's been reasonably popular when I've brought it up before.
I'll give you the short version. Men and women date for different reasons.
Women date to find someone to spend their lives with. Men date to find someone to spend an evening with. And my theory for why disparity exists is that womens biological clock ticks faster than men.
For women, at the back of their heads there's always "I need to be having kids by 35, which means I need to be married by 32, so I need to find a man worth marrying by the time I'm 30." That makes every single relationship a big risk. Are you wasting time with this guy when he's going to let you down. Every first date involves you thinking about the future.
Men don't have that pressure. We don't need to settle down until we're 50 if we don't want to. So we don't spend that first date trying to evaluate whether we want to spend our lives with the person opposite with us. The furthest we're looking into the future is "Would I like another date with this person". We're not looking for someone to spend out lives with, we're looking for someone to spend next Tuesday with, and then if that goes well, maybe Saturday, and then Sunday, and then... Long term relationships aren't something we go looking for, they're something that happen to us almost by accident.
And it means dating for us is fun! And I don't just mean the sex bit, but the actual date bit. It's fun to spend a few hours out for a meal or in the pub or out for a walk, getting to know someone new, finding out you fancy them, finding out they fancy you.
Ok, that wasn't really the short version.
So here's the thing. You want to date, but you're trying to date to find someone to spend your life with. You don't have time for that, and won't for a good 5 years or so yet. But ironically, the very thing thats stopping you finding your partner for life, is the thing that's freed you from your other time constraint. You've had your kids, you don't have that biological clock ticking down to 0 any more.
And that means you don't need to date like a woman any more, you can date like a man, for the sheer fun of it.
There are plenty of men who will be happy with a lunchtime date once a week, and not just shit men either. Men who don't have a lot of free time, men who have their own caring constraints. Men who work weird hours.
Are any of these likely to turn into the person you're going to spend the rest of your life with? Probably not. But you don't need them to be, you've got years to find "the one". For now, you can just date for fun, spend an enjoyable afternoon here and there. Most of them might only last 3 or 4 dates before you or he get bored, but why does it matter, you don't have time for a proper relationship anyway. Maybe you find someone you want to kiss, maybe even have sex with after a couple of months. Maybe you even find someone who you're happy to have a very casual relationship with for a while. You get a bit of practice in, you get to have someone other than your ex be your last romantic partner, and most importantly, you get to spend a few enjoyable afternoons with some nice adult company.
And then, in 5 years or so, you can start dating like a woman again if you want.