AIBU to think that many parents with children think the train belongs to them and that their sleeping bubba gets priority over, well, anything else and everyone else on the train and if bubba wants to "chat" then every other sodding traveller has to listen and look interested?
Welcome to real life OP. Most people will not be rude about you and your children travelling on public transport. Some people will help you. Some people, usually I find those same middle-aged women you seem to vilify so much, will actually sit and listen to the inconsequential and frankly piss boring "chat" that comes out of a 3 yr old's mouth. Because your children are the centre of your world, no-one else's.
And what's with the shouting and telling people off saying you didn't mean this, and you didn't mean that?
The title of your OP is fairly clear. And very entitled.
I have been that mother on public transport (don't drive) but now, yes, I sit there watching the mother with the buggy and the 3 yr old thinking "please not here, please not next to me". Why would anyone choose to sit next to a 3 yr old? I'm not unkind, and I would help you, and I would probably briefly smile at your kid. But I'm not indulgent and am not about to waste my entire journey pandering to other people's whims.
And I believe the first rule of polite crowded public transport is that no matter what, the buggy gets folded.