I agree that these are actually big problems, and its obviously grating on you already.
You seem very clear about parenting techniques - impressively so in fact! I do wonder if this might be making your partner feel a bit rubbish if she's noticed this gap between your skillsets?
It's also alot harder when you're doing it day in day out and on your own, so shes probably exhausted and doing really well in that context. She sounds like she's got quite a different style of parenting, and may actually want to be more relaxed and go with the flow.
You do need to sort this out and I'd maybe start by asking her what she thinks about it all - does she want to change? As if she doesn't, there's no point in pushing her, even if you think it would help her.
Oh and my last thought, the Ds is two yes? I'm not sure why but I feel a bit uncomfortable with the way you keep saying 'manipulative crying', it seems a bit of a harsh way of looking at it.
Yes two year olds are manipulative in that they are learning that they can have some control iver their world by doing certain things, so he gets a certain result by crying, but its not a bad thing at all, as that goes for speaking too, he gets a certain result by saying 'mummy cuddle' or whatever too.
He's very little and just learning how to interact with the world, and a word like manipulative credits him with a bit too much intent, and makes him sound like he's being very naughty, which I don't think he is.