Hello. First of all congratulations for breaking free from your abusive H. 
That's something to be very proud of, it's not easy, especially when you have DCs to leave a controlling relationship, so whatever happens now you will be in a better place to take care of yourself and your baby.
It will depend a bit on whether you are in a tax credits or Universal credit area I think. The rules on self-employment under UC are a bit harsher from what I understand, i.e. they will expect your business to make at least minimum wage for you from the beginning, whereas with TCs even if your business made a loss or made you less than NMW (which many small businesses do for a while) you would be eligible for a top up.
I am a self-employed single mum, I have 3 DCs and have always been self-employed even when married, so don't really have any experience of working for anyone else! I do get tax credits if I don't make enough money from my business, but they do require lots of proof of the hours you are working, your accounts etc so there are some hoops to jump through. I also get council tax reduction and they are even worse for wanting all the ins and outs of my accounts for proof of income.
However for me it is well worth it to give me the flexibility to be home for my DCs after school and during the holidays. Once they are all old enough I will look at other work, but for now, I get maintenance paid by my ex, I get income from my businesses and child benefit/tax credits, which add up to a liveable income.
I'm not sure how it works in a job like cleaning with a baby - presumably you'd need to pay for childcare there too, as you couldn't take them along with you. Do you have someone who could look after the baby in this case?
I pay £12 an hour for a cleaner, I provide materials and she does my house in 2 hours (not very thoroughly, but all bathrooms, floors and dusting, which is all I need to keep on top of it really). Anywhere from £10-15 is probably average but bear in mind that it's pretty physical work, so you probably wouldn't want to be doing 8 hours a day, you need to factor in your travelling costs between clients, you don't get paid on the days you/they are on holiday or when you/your baby are ill, so this needs to be factored into your calculations.
With your other job you would be able to get childcare vouchers which means you pay an amount into a voucher scheme before it is taxed, so if you're a higher rate tax payer you would save a bit there.
To be honest, running a business from home with a young child is a headache - you are constantly feeling guilty that you should be out with the baby somewhere when you're working and that you should be working when you're at the park. There would always be some big noisy drama the minute I was on the phone to a customer! And you can guarantee they need the loo or a nappy change the minute you try and get on with anything important.
However, it's good for them to see you working and earning to take care of them as they grow up and I think my DCs have a lot of respect for the fact that I am able to run a business and support the family while also being here for them when they need me.