Am I wrong

Me and my partner have 2 children 9 years old and 3 months old, our eldest was playing on the floor and I asked her to do something twice and she didn't, I then sat sorting baby out feeding and settling baby, was about to go shop and he raised it with me how I failed to follow through and that I missed that she hadn't done what I asked. I said to my partner why didn't you step in and back me up, he said why should he, I should have been paying attention and followed through, we ended up in am argument and I got away with him,(wrong on my part I know, I was so frustrated) I have the kids all the time unless eldest is at school, I do everything around the house and cook aswell as do everything for the kids, he goes to work from 8-5,.I'm on leave, doesn't spend much time with the kids at all, had a few mins snuggles and it's back to me doing everything again, he doesn't settle them to bed, do the last feed, he comes home and sits on his Xbox till half 12/1 in the.morning. I came back downstairs and asked to resolve the situation again he shouldn't have to be back me up because the 9 year old listens to him and she doesn'te because I'm always inconsistent, I said about finding a common ground where he has my back and again he said no as it's my own fault. It's my default. I snap at home when he comes and raises something. Yes I do snap because I feel alone and like I'm a single parent yet he gets to sit relax and unwind,yet I have to carry on until I go to bed. I don't get any unwind time or me time. So yeah I have snapped at him, he tells me I need proffesional help, go to school again and open the first page of parenting. I said to him many times before this is why I never come to you because you always put me down, tell me I'm incapable or its impossible for me to be at his level. I'm so low and when I tell him how I feel he says all I ever do is put my feelings first never anyone elses, your with someone who's depressed and suicidal and all you think about is your feelings. Yet refuses to seek help and me there supporting him,He makes me feel so guilty and question myself and I am the one always apologizing and saying I was wrong and I will change. Advice ladies Im at the end of it tbh