If your husband was raised in an environment where one of his parents would come home in a bad mood, his behavior may be a little more difficult to change because it may be embedded in him. He may be playing out what he experienced, making your conversation with him potentially tougher and more sensitive. If this is the case, the conversation still needs to be initiated with the abovementioned “I feel” script. (You need to tread lightly, as people often do not take well to criticism of their parents or themselves.) Another idea to ponder is your husband and you coming up with a silly word that you can say when he unknowingly comes home cranky. This can help him remember your plan while making the mood lighter.
Try to have dinner ready (either by cooking during the day or the night before, or ordering in if that’s easier) and the children somewhat calm when he comes through the door. I understand the challenges of the after-school rush, so I know that more work at that time is difficult if not impossible. So try to reprioritize what you need to get done.
As for the children’s homework, it might be helpful to have them do it right when they get home. Give them a special snack as an incentive to complete their homework. It would be beneficial to keeping the home situation calmer while you make whatever changes possible.
With summer here, now may be an opportune time to improve the situation, as your husband’s hopefully better mood upon returning home from work may extend to the school year.
Finally, if all else fails, you should seriously consider seeking professional help. If your husband is experiencing depression, which may be manifested by his anger at the children, medication may also be something to consider. This idea should be discussed with an appropriate professional. Please keep me informed if any of my suggestions were helpful as you confront your challenging situation. Hatzlachah!