NAB
I have children the same age as yours. They exhibit similar behaviour - they fight, squabble, shout, can forget their manners, can get angry for no reason, and some days they make me really cross, sad, frustrated and disappointed, and I cannot wait for bedtime.
However, I know that I am a good parent. They are lively, clever, interesting, imperfect children. Other people may have got better behaved children - lucky them. I got live wires (well, 2 out of the 3 are). However, I don't see their behaviour as a sum total of my parenting, and I know they would be ten times worse if I was a worse parent.
Some children are just hard work. I do envy parents whose children are easier to deal with, but I know that they were lucky rather than better than me.
So, I agree with the PP. You need to allow someone to help you see this. It also sounds like you expect yourself to be a crap parent as your parents were too. The fact that you care so much shows that you are not like your parents.
Please see your GP about getting some counselling. It is not an admission of anything, other than you saying that you want to improve your life.
Seriously, you have a lot to be thankful for, but aren't in a mindset to be able to enjoy what you have. Some talking therapy may be painful, but could do you the world of good I am sure.
Yes kids can be a PITA and cause you to question yourself, but if you can build up your reserves a bit, you will find it easier to deal with the crap and get some more joy into your life.
Please takes all the suggestions here seriously - you are not crap, you just think you are, and you can change that