If you trust them enough (see rule #1), you can get into details about your fears. Let them reassure you that it’s OK and you can still go on dates.
Try to understand what they have in mind when you raise such a discussion and mind their body language. They probably still thinking about it and they are not clear about dating.
If your partner’s children are younger than 10 years old you will have better chance to be liked.
Kids are more approachable at this tender age and you can be their new friend. No matter how sweet it might sound, you need to stop it right away.
If they are in love, you have nothing to be afraid of.
Avoid saying nasty things about their mother of father. On the contrary, you might end up being hated for trying to get between them. Don’t position yourself opposite them because either way you will lose and you don’t deserve this.
If you are dating someone with kids, you have to accept that everyone has their own role in this love game. You are an independent person with your own qualities that has a great personality.
Kids needs to know that they only have one mother, and that’s not you.
It’s their biological mother that has given birth to them.