Does he agree, as you do, that the yelling and such is not good for the kids? What are his thoughts on both of you together, seeing a professional?

Because if he can agree that the yelling that's mostly coming from him, in addition to the parenting inconsistency, is not good for the kids. Just based on that, is reason enough for both of you to seek professional help.

Anyways, maybe that's not needed now since you did mention things cooling down. But perhaps just sitting down with him when both of you are calm and addressing your current concerns (And his, I suppose) is something you can do if you haven't already.