You are not a shit mum. You are a great mum, but he is a shit dad.
Of course it's not simple. You have been together for more than a quarter of your whole life, and your whole adult life.
Okay, you have no qualifications, but you are young enough to get some. What would you like to do?
Or, if you really need to start earning money, now, what about taking in people's ironing? My MIL did this for many years, and she always said it was the only job she could do at 6:00 in the morning, (or whenever) in her nightdress.
When your little one is at nursery, you could ask around your ironing clients to see if they know someone who needs a cleaner, and add that to your repertoire. When your little one is at school, you could continue with that, and start to do some evening classes at a college.
I suggested bookkeeping, because it's another thing you can do from home in your pyjamas, although you would need some proper work experience, before you could get to that stage. I understand that there is a shortage of people training to do bookkeeping, too . There's also excellent career progression, if you wanted. Working in a school may work well, as you have less holiday cover to worry about, but there is the disadvantage of not being able to easily take any days off during term time.
Or is there something else, you would really like to do? Having children does limit your options, no point in pretending, but there are often ways.
You really can do this.