I can imagine if a child has two fairly permissive parents, there are all kinds of disturbing behaviours that will follow because they've taken on an alpha role over their parents. Especially by 10, a kid could be pretty difficult to deal with.
Gordon Neufeld has done some excellent work on this and on the kinds of behaviours that occur when the attachment relationship is turned upside down. He also talks about how to regain the alpha role as a parent so that the child can feel secure and also start to mature emotionally.
This is a huge undertaking! Although it can be done, it's not a quick and easy fix and your bf has control over very few of the other variables in the boy's life. If it were me, I don't know if I'd have what it takes to stick with him for the rollercoaster that is sure to ensure over the next years.
For your own sake though, you need to think about what has changed since your bf was willing to be casual sex partners with a woman (over the course of years) when neither person discussed the eventuality of what they would do should a pregnancy occur. How he got to the place where he made some of the choices he has is very understandable, given his childhood circumstances. Unless there's been a major change involving therapy etc, and evidence of behavioural shifts for some time, it doesn't bode well for building a future together.
Often people feel like if they get the trappings of a good life, it will somehow make everything work. However, without adequate preparation and a solid personal foundation, it is easy to fall into a dysfunctional dynamic in a romantic relationship. You might want to think about why you are willing to accept a partnership that is built on shaky ground. It may mean that you both need time apart to prepare for time together, or it may mean that you are getting your needs fulfilled in some way by having a partner who needs you desperately. It's better to at least be consciously aware of what you are doing and why. In a sense, I think the kids are only a symptom of a much bigger issue between you and your bf.