I would imagine you would mostly be meeting men who are divorced or separated with kids themselves so ... What does it matter?
If you got serious and he's any kind of a father at all, he'd be having his kids some of the time ... So you'd both be bringing kids into the relationship and you'd both be blending families eventually and you'd both be expected to become step parents to some degree eventually.
So you're in a similar position.
You're not bringing anything or expecting anything that he's not!
Men with no kids yet themselves ...yes, I could understand why they may not want to get into a relationship with a woman with kids.
However that's not to say some will not.
As for sex....I haven't had full penetrative sex with several of my ex partners/current partner until months into the relationship.
This will weed out most sex seekers.
Of course there may some who will date for a few months, have sex and then dump but most sex seekers will simply not spend the time or effort or money on dating regularly for months - if they're only after sex. Most will just go elsewhere to try to get it quickly & with less effort.
You can just say you've only had one partner (or whatever) and you don't rush into sex with someone and you're the type of person who prefers to get to know someone well before you have sex etc.
Most people who like you and want a relationship won't be put off by that.
Don't go on dates and drink/get drunk ....that's a sure way to have sex quickly because it lowers your inhibitions and raises testosterone in women which makes them horny lol.
Avoid drinking much or at all.