Yes, will be living here once baby comes due to continual saving. Separate issue is I work for my father's business on minimum wage so don't financially earn enough to get a high enough mortgage despite having substantial savings, and my partners hours have just been cut
Do you have other job opportunities?
Could you afford to rent?
Honestly, Covid is probably going to take care of this one, especially if you're due this year. It's unlikely that you'll be allowed more than one birth partner, and most places don't seem to be allowing visitors either.
But overall, you're in a very sensitive position when it comes to your parents. Your Dad employs you, and your step-mum is already feeling a bit overbearing about the baby... Living at home sounds like it could be a recipe for disaster, even before you add in a crying baby and hormones.
I'd be looking for solutions here. The easiest way is probably going to be to stay working for your dad, but go rent somewhere - use any excuse if you have to, say that you want to be a proper "family" before the baby arrives and live just the three of you. Then you can change jobs down the line, if you want to.
But as it is, I'd be worried.