Vicki88 I wanted to offer you a supportive post in this situation - given that you are where you are in this situation. yes getting to this point quickly may be less than ideal, but I am sure that you have done it with the best of intentions and I think many of the posts here are less than helpful in offering advice for the next steps. I don't think passing judgement on you will help any, tbh!
I am without children and about to move in with my partner who has a SD half the time living with him. I know the SD and we have our ups and downs, mostly ups, but there is an unwritten thing going on at the moment between us that the relationship between me and her will move to a whole new level when we share a house. We both have trepidations about it but we will both work at it and I hope that it will be a good outcome (I think parts of both of us are also secretly looking forward to it). But: we will not be able to make it work without my partner's active support and involvement. It's new for him as well: but he needs to man up to this, and to his responsibilities.
I think your idea that I feel like this is something that I shouldn't need to ask him and that he shouldn't need persuading to do - it should be automatic... is misguided, and it's causing you trouble here.
There is a lot of learning for you, and your (newish) partner ahead of you if you are to make it work - and work to the benefit of the kids as much as benefit to the both of you. You need to get conscious of each other's perspectives, and quickly, and start talking honestly: swallow pride and think about conscious time to get to know one another, ground rules, positive solutions to difficulties, and giving space for each others' needs. At the moment, it sounds as if you have made assumptions about how he should behave, and assumed that everything would just be OK (I think this is meant to be a fairly common reaction) - but it just doesn't happen like that unfortunately.
I think what a lot of people on here are articulating, albeit unhelpfully, is that it is far better to work these things through before you move in than when you get there - although most people on here are coming only from the perspective of the kids' welfare - while this is essential, it's also really important for the relationship.
so how about the situation from your boyfriend's perspective? (I am far more qualified to talk about this than the kids' perspective) I think a lot of people with kids are so used to their lives with kids that they forget: the perspective of someone without kids is just as valid. Getting together with someone with kids is difficult. Have a look at the Step-parenting board to get an idea. There are many mothers on here who will flame any poster who dares to suggest that step-parents (for want of a better word) have any rights at all: but think about it from his perspective. he is unlikely to see your kids as a bonus to the relationship, he may be scared of relating to them, unsure of what to do, just non-plussed; he may be feeling sidelined in favour of walking evidence from your past relationship. These are all really valid feelings. He needs your active support to build good relationships with the kids here and to make it work. Yes, he needs to be willing to participate as well, but if you haven't even asked him or talked about the kids with him - if you're not working it together - then you're not giving him much of a chance.
To be honest, if my partner expected me to start engaging with his kids and assumed I would be happy taking on more of a parenting role without even discussing what he was asking me to take on or supporting me with it, I would have big alarm bells ringing: not about the kids, but about my partner!!