i wouldn't leave or ask him to leave. i don't think classes are particurlarly helpful unless the person is motivated to look at themselves and make changes if necessary. i do think it needs to be addressed for you and your relationship, and for your babies.

i would talk to him, see what's going on, see what he thinks of what happened.

My first was a needy baby, but i was in a whole lot more of 'this is hard work' when #2 came along. DH walked around with earplugs in his ears (to dull the reflux baby screams) when he was around 2 months of age. I don't like it, and am working on it, but there is a lot more yelling in this house since #2 was born. And sometimes it is just because we are at our end and don't know what to do. Sometimes, having the other parent remind us of how we want to parent, and give support and acknowledgement of the difficulty makes all the difference.

I would be concerned about a child being hit across the back of the head, but if it was reflex and the person realised they were wrong (without being told it) my reaction would be different to if they thought the action was justified and wanted to continue doing it.

When your toddler hits or hurts your baby it can be really confronting, cos both of them are your babies but one is hurting the other.
I agree with the 100%.

Since having DS, a lot has changed in our household. We both have a strong need to protect him so if DD hits him during a tantrum she is punished, we don't her hurting him at all lightly and we have resumed with smacking as a form of punishment as we have found she will just continue to try hit him or even hitting him which is not fair on him at all.

I do think you need to sit down and address this, find out what is going on as obviously if his actions are out of character then there is an underlying issue.