@GreenSlide
I think it would have been better for you to say something like, I was only driving at 15 mph, but don't worry I'll definitely keep an eye out for your child.
You've just escalated things really and I don't think they needed to get that bad.
I think something like this would have been the most reasonable response.
It's clear you don't like these neighbours and that's okay, we can't like everyone. I have a neighbour I cannot stand, he's rude and goes out of his way to piss me off (small things but obviously done to irritate or intimidate). And honestly, if he asked something of me I'd likely also want to say no because the idea of complying with him is unpleasant, but it would depend on whether I thought it was a fair request.
Hard to comment on whether your speed was reasonable as no one here knows what your street is like. On my street there are sometimes kids playing and cars parked where kids could suddenly pop out from, so I'm usually doing no more than 10mph, but sometimes it's a little faster. Not everyone will agree on what the 'right' speed should be, and no they can't make you agree with them and act in line with their views, but it's not unreasonable to worry about the safety of your child and ask.
Perhaps try and turn it around? Of course they should be watching their child, but accidents happen and, I don't know about you, but I've fretted over all the things that could happen to my beautiful daughter who I love more than anything. Imagined terrible things happening and got myself really anxious because something happening to her is my absolute worst nightmare. And if at a moment when I was imagining something like that, seeing a neighbour drive - what seemed to me - a bit too fast, I might (with quiet terror inside for my beloved daughters safety) ask them to drive a little slower, be a bit more careful.
Maybe your neighbour is just trying to piss you off, or demand something 'reasonable' from you to force you to comply etc. But maybe, they really are just worried about the safety of their dc. And if my neighbour that I really don't like, drove (IMO) fast on our street and I asked him to please drive a little slower because I was worried about my child, and he just said no, with no discussion and (seemingly) no consideration for my request or the safety of my child, I'd be pretty pissed off. I agree your neighbour shouldn't have shouted at you in front of your child, but I can also imagine getting cross and shouting at my neighbour in that situation (though not in front of their child - though he doesn't have one). It's always ideal to stay calm and have a reasonable discussion, but emotion sometimes gets the best of us.
Sorry for such a long response! I hope you manage to eventually have at least a civil relationship with your neighbours. Perhaps you could try one last time to be the bigger person - go round there, invite her (?) and her child round for a play date and take the opportunity to have an honest discussion about everything. Perhaps it will end with you both hating each other, maybe just maybe you'll gain some understanding or common ground. I personally don't feel like you'd have anything to lose in this situation (if they were shitty I'd just feel better about myself as a person!) but I appreciate that actually doing this would be very unlikely, so it's just a hopeful positive end to my input/advice 😊