Regarding the bolded above:

I think it's natural to question people's trust, if you have abuse in your past. I still question people's trust, due to my own past abuse. And I'm in my mid-40s, and have done therapy for the past abuse and trust issues. What I've concluded is this: trust needs to be earned, not freely given.

And your concern over your boyfriend's anger could be tied to all three outside influences; your family's concern, valid red flags you've seen from his behavior (the sulking, the silent treatment), and your own intuition.

Now that you've had an open discussion with your boyfriend about how his anger effects your relationship to each other, it really is up to him to change. If he chooses to sulk and give you the silent treatment after an argument, which is not a healthy way to express anger, then it's up to you to decide if you want to stay with this man and have children with him, or to end the relationship now, after just two years, and eventually try to find someone who expresses their anger in a more healthy way.