Hi there
I think that calling him all the names under the sun and writing him off as 'abusive' is very easy, but not necessarily accurate.
I am in no way saying that he was right for shouting at you, but if it were me in this situation, I would attempt to understand the underlying feelings that caused him to act in this way.
That is how I would like to be treated had I shouted at my partner. I know that, when emotions and insecurities at the core of my being have been hit, inadvertantly, by someone else, I have shouted and cried and screamed and been desperately hurt. I am not proud of these actions but am very lucky to have a DH that bears with me and has faith in me and invests his love with me to heal me. I do the same for him. He has said some awful things to me in the past, but once I proved myself to be on his side totally and completely, this completely stopped and we are now able to engage in deep conversation about our deepest fears/worries etc that caused us to behave in these damaging ways. We were wrong, but we were forgiven, and we made our relationship become extremely deep and supportive through this understanding. Our relationship has always been extremely loving right from the get go, but with these periods of extreme emotional difficulty. These have been decreasing slowly and steadily and are now extremely rare, and we both agree that we can see them completely gone within a couple of months.
With my ex there was a similar situation, but I was so hooked on him being 'abusive' that I spent all my time trying to change him and never understand him. Looking back, I was just as abusive as he was, but I was completely unaware of it and perceived myself to be a 'victim'.
People will say that 'walking on eggshells' is a sign of abuse. I have found that sometimes it is and sometimes it isn't. Sometimes, there is a huge gulf between the understanding of a man and a woman and their emotional needs. Learning to understand these is to me very important, learning how our behaviours, maybe even tiny ones, have effects on the emotions of others. This is not to say that we should become a prisoner to the insecurities of others, but rather that we should act out of consideration, rather than a defiant claim that 'we should be able to do as we please.'
My initial instinct, which you confirmed later, was that he was upset because he saw himself as part of your family now i.e. that you were no longer a single parent because he has taken the DC on. I could imagine that you going to this picnic without an explanation (which I do not think was wrong in any way) could have caused him to panic a bit, as it could be read as a signal that you don't take his involvement in your life as seriously as he takes it. That may have been deeply hurtful to him, but as yet you as a couple have maybe not set up channels of communication sufficient to share such deep feelings.
If you feel that you cannot put up with shouting, then that is your call. But if you feel you can be patient and try to understand his feelings and maybe find a way to talk about them openly, there could be a possibility of the forging of a deeper relationship. Alternatively, there might not be.
As long as you have a grounding sense of who you are outside of him, for example, children, family, passions, interests, drive etc, it may be worth a try. I suppose it depends what kind of relationship you want.
All the best