You are asking good and important questions. Those questions are so good I am surprised you actually moved across states to move in with your guy before you answered them. His children are a fact in his life. Being with him means you have children – two of them. They are going to be a central part of your life and his for at least 20 years. If you move any further into this relationship, you’re a mother. It looks to me like you didn’t factor that into your decision-making.
I think you should take your own good sense seriously. Asking the question about meeting the children is a way you are asking the question about whether you want to enter your boyfriend’s life. At 30, he is at a different life stage than you are. Some women (and men) like the opportunity to fold themselves into a lifestyle that is already pretty established. But others like to be with age-mates and discover how life unfolds together. It looks to me like you are having your doubts.
You owe it to yourself, your boyfriend, and the children to take a step back to think about all these things before you complicate matters further by being introduced to the children. Young children love easily. It’s not fair to them to get into their lives if you’re uncertain. They’ve already had to manage the breakup of their mom and dad.
The fact that you are thinking hard about the implications of meeting the kids tells me that you are a thoughtful and sensitive person. I suspect that you got so swept up in love that you lost sight of some of your central values. You’re now at one of those moments where a decision will take you down one path or another. That deserves some time and consideration.
I wish you well.