Imagine that you dated a single father and became a step mother to his kids.
Of course they might like you and be attached to you.
You might miss them too, right?
The thing to remember in these situations is that his kids are part of HIS reality.
Sooner or later, he will meet someone who will be the new step mother.
How will this make you feel if you realize you are now competing with her even on that level?
I know it is tough to say but you own them and him nothing, ok?
Legally, you have zero rights.
When he breaks up, you are no longer part of any decision making process concerning them.
Let's fast forward to a year later...
You met someone!
This guy is great and he likes you too!
How will he feel when he knows that you are still invested in your ex's children?
What if he has children too?
What if he is the one invested in his ex's children and they see each other a lot because of that?
How would THAT make you feel?
See the dilemma and the conflicting interests?
It is normal to dissolve everything that is related with him when he breaks up, not just the direct relationship you had with him.
To your power!