I don't think parents shouldn't help their DCs, but the OPs parents have - her dad has taken out a loan on her behalf because she couldn't get one, she has to pay it back as if she would if she'd taken it out herself - although she claims her dad is rich, the fact he took out a loan rather than directly loaned her the money suggests he doesn't have stacks of savings (most people in that situation would use savings rather than have a loan in their name), she assumes she knows exactly what he earns and what his outgoings are so he can afford to just give her £70 this month. I wouldn't be so sure.
I would assume it took you 6 months to wear him down to agree because he thought you'd do this - he knew what you were like and thought there's a good chance you won't pay the loan. I would imagine you have 'form' for being crap at paying back debts if your credit rating was so bad he had to take out the loan in the first place. Have you got a history of just not paying things back and expecting it'll sort itself out? That someone else will pick up the tab eventually and you shouldn't have to pay your debts? This is your debt, not your dads. You don't owe your dad, you owe the bank he borrowed the money from.
Could his comment about the baby, while horrible, come from a genuine concern that you and DP don't seem to be able to cope financially with one DC and really not understanding why someone in such a situation would decide to have another?
Next your mother - you asked her to look after your DC so you can go on holiday, but you're angry she's not available to do so because she's going on holiday with someone you don't like, but she does, she's an adult, it doesn't read like she said she would have your DS, let you book the holiday then said no, she said no as soon as you told her about the dates as they clash with her holiday, did you really think she should cancel her trip as yours is more important?
I find it very hard to believe your PIL bought you a holiday with no discussion with you first, you haven't got any spare money (if you can't find £70 to repair your car, you can't have any savings), you are pregnant again, but rather than saying "actually we're really struggling, it's nice of you to offer the holiday, but could we have the money instead?" you and your DP said yes to the holiday - a holiday which is just for you two, not your DC, and they are only offering free childcare for some of the holiday they have bought you, but knowing you can't afford to pay for childcare for the rest and the only alternative is your mother, yet no one thought to check the dates with your mum before booking it.
Can you not see you should have said no? Or at very least checked your mum could actually do these dates before anything was booked?
I really think families should help, but there comes a point when really, you have to be prepared to help yourself at least a little bit. OP, you come across as expecting your parents to fit round what you want, you want your dad to just give you a car and are annoyed he expects you to pay for it, you want your mum to just be available to do childcare the way you want when you want, without daring to have plans and a life of her own.
For the trip, if you can't cancel and get the money back (which I would strongly recommend you do, having at least a couple of hundred quid saved might make the world of difference to your life), then talk to your PIL, they booked the holiday without having confirmation there was childcare in place first, why can't they do the whole time? Or are they being equally annoying and having a life too...