Hi Mat,
There's a lot to unpack in your post, and I'm not surprised you are exhausted and angry. I don't entirely understand why your renovation work has driven you into separate bedrooms, but it seems to me that the strain of having a young child in the house has come as a bit of a shock to you. Don't worry - once toddlers emerge from their impossible stage, most of them turn into very nice little children and it becomes very rewarding to parent them. (Crossing my fingers here you don't have one of the really difficult ones).
Your wife has done an appalling thing in tricking you into getting her pregnant. It's a betrayal of trust, and I think you might both benefit from some marriage counselling, if you can possibly find time and money for it. Meantime shouting at her won't help - I can tell it is making you feel miserable to be losing your cool like that. Whilst your anger is understandable, you need to find better ways to disperse it.
I do think your exhaustion and anger may be stopping you from being pragmatic about your problems. You are letting it all pile up in a mountain instead of breaking it into bitesize chunks. So let's stop and think what your options are, and what immediate actions you can take.
First you need to simply tell your wife that YOU are managing the renovation so yes you'd love her help but she must ONLY do exactly what you instruct her to do. Tell her the best thing she could do right now is give you some relief from weekend and evening childcare while you break the back of the work. Can she go and stay with relatives for the next several weekends? Could the toddler go and stay with grandparents for a few days? Can relatives come and help with the renovation work?
If you do in fact walk out on your pregnant wife and toddler (which, despite what your DW has done, seems like quite a shitty thing to do, especially to your noisy-but-blamesless toddler) then the house would presumably be sold quickly. Your wife couldn't stay in a half-renovated house with no heating and two little children for long. So...If things are absolutely desperate, why not simply sell the house now, abandoning the rest of the renovation, and stay together by moving into a smaller place or a rental, which is actually finished?
Money worries. Is your wife currently employed out of the home, or is she a full time mum? Maybe when the baby is 6 or 9 months old she would consider going back to work full time, if the finances of that make sense. Sometimes it is simply cheaper to stay at home with both kids until the eldest is in school. Have a calm discussion about it and explain the extent of your anxiety about finances. She .right have some ideas up her sleeve but is afraid to mention while you are whirling around on the brink of fury and breakdown.
Her "days of not talking to you" are probably driven by guilt, not wanting to provoke you, anger/frustration that you haven't just come round to seeing things her way, and feeling unwell. She might be terrified that you are going to walk out, and crying herself to sleep every night in the spare room. She might be regretting getting pregnant. She might be worried about pushing you over the edge and you having a breakdown. She might be feeling cross or surprised at you for not seeing things her way. She might think you are exaggerating the renovation troubles as a smokescreen so you can avoid addressing other problems in the marriage. Do you know how she feels? Isnt it worth finding out? Have you actually tried sitting down to talk this through?
Having a second child you don't want is a horrible prospect. Toddlers are immensely hard work. You have a lot on your plate. You have my sympathy. But you need to do some adulting here, take a deep breath and talk to your wife.
Your problems, frankly, are not insurmountable. So if you want to be in your kids' lives, you need to fix things.
Rember now things are tough but in future there are positives. Two young children will play happily together and that means less work for you in the long run. An extra child doesnt cost much more especially when they are close in age, although it may delay your wife getting back to work. And if you can get through this with your wife, as a team, instead of allowing it to destroy you, well I reckon you can get through anything.