Lol what? There is only one thing tighter than your dear partners arsehole right now, and that is a Chinese finger trap.
With all due respect, you are needlessly, financially impoverishing yourself and it's really sad.
You're pregnant and you already have a child dependant on you. It's so important that you hit this nail on the head now, because unnecessary stress is not good for a developing baby, and it's really not good for you either. All of this stress can be avoided!
So he has two jobs (from which neither currently yields a penny to your household), one which pays a wage into his bank account, and one which he 'does on the side' for extra cash, which also mysteriously disappears every time he accrues it? That sounds pretty dodgy to me to be honest.
I assume he isn't doing his self-employed tax contributions correctly either if it's cash in hand and he can't provide a record of it.
If you can't squeeze any maintenance out of him, you could always threaten him with HMRC... ;)
Okay, so that means that he does have some kind of record of his wages for the other job at least. Get ahold of these statements and look at where the money is going. Like I mentioned earlier, work out how much your house is currently running on and what is needed from him to help supplement that. Don't forget, If you are cohabiting with him, then your bills are also his bills and he needs to help pay them. Otherwise, he needs to GTFO. It's simple.
YOUR Benefits are affected
As a full time mum, with no job and no support from your Leech, I'd assume that you are living on benefits?
Don't forget that the amount you can receive in benefits is directly affected by both your income (which I'd assume is 0, because you're a full time mum), and your partners income. This is all calculated when your housing and social situation is assessed. In simpler terms:
Because you don't work, the money you currently receive in benefits is calculated based on how much your partner is bringing in.
If that money is not being provided, then your benefits calculation is grossly undervalued, and you are not receiving the support that you should be - because you aren't getting the money from him - the extra money that that calculation is based upon.
The money is not flowing into the household as it should be. This is a huge problem for you... So stand your bloody ground. If he isn't paying, it's directly affecting how much support you can get - how much council tax you have to pay, how much rent you have to pay etc...
He either pays, or he needs to go.