Your problem is an (understandable) lack of confidence and belief in yourself. You are doing a brilliant job, you don't sound as though you are putting a foot wrong. The dynamic between your children sounds entirely normal to me.
One strategy I tried for coping with tears and tantrums and endless endless sibling bickering was detachment. It works like this. Picture a video camera in the kitchen, or wherever you are, recording the goings-on. Then watch yourself dealing with the incident as though you were watching someone else in a reality TV show. It really helps you not getting caught up in this stuff.
Also, have some stock responses for these emotional jibes - they know all your buttons, remember, so don't let them push them.
Stock response 1 - To the "I don't love you" comment "That's a pity because I really love you".
Stock response 2 - To the "You don't love me" comment "Gosh, you know, you're absolutely right. You got it. I don't love you a bit. Not even a little bit. I'm just doing all this caring, and feeding and refereeing and ferrying for my own amusement."
Stock response 3 (my personal favourite, and on good days, this gets them laughing) - To the "It's not fair!" comment "Into each life, some rain must fall."
Stock response 4 - To the "You love extra room."
Or something. The importance of having stock responses is not so much what they are, it's to bring them back down to reality. They mustn't vary. Stock responses work a treat at diffusing mild to moderate situations that look as though they might escalate.