I'm the exact same way! Not everyday but a lot of days I get like that. Mostly with my 5 year old in the mornings before I drop him off at school. I'm already exhausted because I sleep porely at night and am not a morning person. I always feel bad probably half way to school, so I try and lighten the mood by playing some of his favorite music or get him to read me one of the books he's working on learning to read during the ride. It's very very hard and I can't imagine throwing 2 more little ones into the mix, just know you're not alone! It makes me feel better knowing there's others who are having the same issues! <3
Hope you get that under control soon without any medication.
How about lighting a candle of your liking that might help you be more relaxed. I find lavender very calming.
Oh my, I haven't been so angry at least that I've noticed, ha! But when I don't eat on time I do get irritable. I try real hard to breathe and not take it out on my two year old or my husband. But I can imagine how hard it could be for you with your kids. So close in age and them being at most active ages might be overwhelming. Try to figure out what sets you off. And talk about it like in the instance with someone; perhaps that might help ease your anger. (If there might be something specific). But either way if you can't figure out what irritates you instead of yelling at your children talk to someone. If I'm mad or stressed I call my husband and cry or yell. Thankfully he is very understands me. Hope that helps if you're not already trying to do that.