You are wise to ask questions and consider the children's feelings...
The FIRST thing New Guy's kid said to me was "You can't marry my dad!" At the time that was not on the agenda yet, but my heart went out to her. So we talked about my nephew who is her age and likes stars and bugs, and then she'd see me on occasion and we'd chat.
Now we spend more time together, and New Kid swings back and forth on wanting us to get married. (Realization: I am good but I am not going to be perfect!) Not that this is her decision, but it goes to show that kids do have a lot of concerns and feelings. My D has gone back and forth as well. There is a sense that the new interest is "replacing" the other parent. The other thing is, you are taking the parent away, in a sense, just by spending time with that person. We had to consider that the children would be stressed if we cut into their time too much. So this has meant our R developed slowly, but it has been worth it.
I am very glad that we let things alone and did not make any dramatic changes. It has been good for the children--I think especially his because they were not fully adjusted to their current lifeystyle when I showed up. They are now more settled and I am less scary. (Or maybe more! But I don't really think so.)
With small kids watching, it was out of the question to move in, and still is. Right now, we spend a good amount of time together on weekends, but we also take breaks from each other, which I think is good for all.
I think step-parenting requires incredible maturity and patience, and I am not always sure that I have it. It will be a shaping experience. I would only want to be a good step-parent who would be reliable, strong, and kind for them--a good influence and loving adult. I do see genuinely loving them, and I think that desire to be effective is important, but I have a definitive lack of experience in this area! Not only do I need to consider his kids' feelings, but my D's as well.
When I get the chance, I will tell New Guy's kids that one of the reasons I found him to be real and one of the things I love about him is that his commitment to them was obvious from the start. For my poor D, she has always had "competition" for her dad's attention. Then when OW moved away, D was deeply hurt. So the fact that your new interest is careful with exposing the kids to you too quickly speaks well of her maturity.
M: 16 years Bomb 4/07 OW 20s long gone Divorced 11/09 I remarried New Guy Cooperative r w/X regarding D