If you can recognise that you may snap then that is good. Put the children in their cots/a safe room, close the door and go and calm down. Or go out/pretend you are being filmed for tv so you become more aware of your actions. Toddlers are the most frustrating thing in the world anyone who has one will understand that.
You can guarantee that ds will tantrum at least once per hour, unless he's asleep! It is so bad that I have to be very careful about the places we take him because it's so embarrassing. I mainly take him for walks in the woods or the park because then at least the sound isn't concentrated!
I have never managed to walk around a supermarket with him without a huge screaming fit (usually lasting the entire shopping trip) in his entire 2.3 years, he won't sit down or sit still, he doesn't share, he doesn't wait for anything. I've never been a parent before, I don't know if this is because of something I have done or if it's just the way he is and he will grow out if it (I'm sure he will, the question is when
).
Do you manage to get any one on one time with your dd and ds separately? That may help with them rubbing each other up the wrong way. Also, is she old enough to help with certain things? (my ds likes helping and it's an effective way of getting him involved and distracting him), so things like helping put the washing in the machine, helping choose the baby's clothes - just little things that make her feel more grown up so she may start to feel less like the baby is infringing on her territory.
It will get better and I can assure you that your dc will never think of you as a bad mother!