I may not have given you life, but life gave me you. - Unknown
First meeting your step children, I will admit that it's very difficult. You wonder what's crossing the line and what doesn't, if you can or can't discipline them if they do something wrong. There are a lot of things you can't help but wonder because technically they aren't your kid yet. The hardest part for me was having the mother still in the picture. It made things tense when I was around her. She constantly was talking to my boyfriend about her daily life, and he talked to her about things happening. I couldn't help but think "are they actually over?" It's especially hard when you don't have a kid of your own, because any time you suggest something that would benefit their kid, they always say, "You never had kids, you wouldn't understand."
This was so frustrating to me—that and the fact that the mother would have multiple guys around her son, taking him to house parties, not coming to see him on time, came when she wanted to, didn't ask for him for weeks at a time, didn't know where she lived, took him on the weekends, stole his baby mementos FROM THE HOUSE! I could honestly go on and on about all the things this girl did to her son. He would often ask when "mommy" was coming to see him again after my boyfriend finally started seeing what I was. He told the mother that she needed to make a schedule of what days she wanted to see her son, and what time she was going to come. Simple, right? Well it would be simple if you really wanted to see your kid. She never contacted us to see him again after this.
Up until this point, my boyfriend just thought I was "being jealous" and almost cost us our relationship.
There's a point where you may have to take some sort of control in certain situations. My best advice is to stay consistent and stand your ground if you feel the kid's life or safety is in hand. If you asked me how long to stay in a relationship where they tell you "you're just jealous," "you don't have kids so you wouldn't know," I would tell you to stick to how you feel for a couple months. If things aren't getting anywhere and they aren't letting you put in your "two cents," then leave. Some people may listen over time, but ultimately it's your call on how long you can deal with that.
Now if you aren't watching the kids then honestly that's just something you're going to have to deal with, but if you're watching their kids then I feel that you should be able to say what you think would be in their best interest, and that they should consider what you're saying. At that point, they shouldn't be shutting you out.
One thing I will say is that you need to treat their kids as your own and not expect to not take care of them when the relationship becomes serious. When you date someone with kids, you need to accept them and their kids. If you feel you can't do that, then you don't need a relationship with them. Those of you that don't have kids, it's super hard to treat a kid as your own if you never had kids to begin with. With time and patience, you'll understand how you should treat them and become more comfortable.