When you have kids from a previous situation or marriage, those children are priority. Kids should definitely be treated as a priority, and they should always come first. Children can't fend for themselves, and they need to be taken care of. Any good parent would put their child above you when it comes to dating.
If you're thinking about dating a single parent, you're going to have to accept the fact that their child or children are going to come first. Therefore, you not only open to dating someone that has kids, but you also need to understand that their children are going to be a priority to them, so their dating schedule might not be as flexible as you'd like it to be.
When it comes to dating a single parent, you should be getting to know the person that you're dating, as well as be open to listening to how they talk about their child or children. The way that a single parent talks about their children says a lot about their character and their style of parenting. As well, it's important to know that someone's child is a part of them, a huge part of their life, and always will be. This is something that you need to be okay with if considering dating a single parent.
A single parent should never try to replace the other parent, despite if they think highly of them or not. I've never been a big fan of single parents that talk bad about their exes. For me personally, that's a huge red flag. Talking bad about others is a definite no-no, but talking bad about the other parent of your children is a red flag. There's a certain amount of respect that you should have for the other parent, whether or not you and that parent get along very well or not.
After a few dates or whenever you feel ready to explore an exclusive relationship with a single parent, you might get a chance at meeting their children. I personally feel that it's best to be in an exclusive relationship before that introduction. It's better to already know that you're in a promising situation that has potential to go forward, before meeting someone's kids. And depending on when a single parent feels comfortable enough to introduce their kids to the person that they're dating, there's something that you should know - they're not looking to replace the other parent.
If you explore a relationship with a single parent, it's important to know that not now, and not ever are you going to be viewed as a replacement to the other parent. The single parent shouldn't view you as a possible replacement to their ex, and you shouldn't view yourself as a possible replacement either.
You should never try to replace the other parent or even think that it's your job or what's expected, because it's not. It's important to know that dating or being with a single parent doesn't define you as a replacement. Just as well, it's important for the other parent to know that you have no intention of replacing them. Being a good step parent is all about being a good role model, and a good parental figure to the kids. As well, it's also about the children seeing the love between you and their parent.
I don't know about other single parents, but for me, if my kids don't like someone or someone doesn't seem to get along well with my kids (Thank God that hasn't happened yet), I won't pursue the situation any further. It's kind of funny if you think about it - When we're young kids, our parents tell us whether or not they approve of who we date. But when we have children from a previous marriage or situation, I feel that it's important to get your kids approval of the person that you date.