The problem isn’t just his anger. The problem is that the two of you don’t share ideas about what is funny, what is appropriate discipline for a child, or how to get the help you need to become a solid couple and good parents. You are not behaving like a committed team. Yes, he gets angry and got physical a couple of times, which is never okay. But you are doing things that he doesn’t see as funny (the frosting and splashing episodes) and threatening him with more of the same.
You aren’t even acting as a team to find a therapist! Why are you waiting for him to make an appointment? If it’s important to you, get on the phone!
I can’t judge whether he has an anger problem on the basis of a letter. I can suggest that the two of you have work to do if your relationship is to last. I think you know that or you would be married by now. So — See a couples therapist. Commit to sticking with it long enough to get a good evaluation and to make some important changes in how you communicate with each other and how you parent. You both, and your child, deserve better than this.
I wish you well.