So as not to jump on any one person, I'd just like to reiterate my stance on dating and kids. Your kids should not be involved in your dating life. They really shouldn't meet your dates until you've been dating for at least 6 months. No matter how great the person seems, you cannot possibly know enough about a person to know where this is going until you've spend some real time with them. And kids DO get attached, no matter how independent you think they are. They don't need to go through the pain of loss unnecessarily when they've already lost so much in a divorce. Dating breakups can and do have an effect on kids, whether it's just giving them the impression that relationships are inherently impermanent or subjecting them to the pain of loss and abandonment feelings.
In the rush of infatuation it's so easy to think "this is the one!" but any adult relationship comes with baggage and potential pitfalls. Ex spouses or girlfriends come back into the picture , or people turn out to be more relationship avoidant than they seemed in the beginning, or they turn out to be hiding gigantic debts or addiction or gambling problems, or they end up like my crazy ex-boyfriend to be carrying on a relationship with an OW the whole time and hiding other things. NO ONE, no matter how savvy you think you are, can be completely sure in the first phase of a relationship and there's no reason for kids to be included in this part of your fact-finding expedition.
Some kids may be more sensitive to these things than others but they all will experience some effect. Heck, my kids were grown when I divorced and started dating nd didn't introduce them to anyone for a couple of years but they are still affected to some degree by my dating.