I too am concerned about his tactics.
Cleverly he asks you how you feel. He can then agree and add to the statements. He never shows his cards op, he holds them close to his chest. You say he is quiet in these situations. Yes by being quiet you fill the gaps, he takes what you say and then uses it against you - mental health for example.
He thinks that him giving you a pittance is his way of supporting you.
Drawing a line in the sand and asking what do you want to happen. I have a feeling he thought you would say 'for us to be a happy family' then he's back in. My first post mentioned tears, anger etc. I think your partner is more restrained. imagine a calmed down version. Anger (ie his email) followed by niceness ( bathing the children) followed by a nasty jibe (ie agreeing your mental).
Get communicating via email and text. You don't want him fighting for 50 % residency to avoid paying maintenance.
It seems that you don't live together does he pay maintenance as per the Csa calculator? If not what was the excuse? What was the £50 he was paying but stopped?
Why did you use your savings on mat leave? Why didn't he just pay for stuff like nappies etc?
Fwiw I am the main earner and earn a bit more than your dp. My dh is a sahd. I pay all the bills, food etc. when he eventually goes back part time, our bank accounts will still be joint, Money will still be joint. He has access to money, savings and credit cards at all times. Saving are put in his name to be tax efficient (I guess the deposit savings are in your partners name despite him paying 40% tax!). All large purchases (over £100 roughly except when buying surprise presents) are discussed regardless of who is buying it.
When you choose to have a child together you don't have as much money, you certainly don't expect the carer of the child to be skint whilst the earner lives the life of Riley.
He is greedy op. His comment when you asked 'what do I get out of this' and he said financial support spelt that out. A token 50 here and there when he can be arsed means shut up asking for money. He believes he is giving you and your dc more than you need, he believes he is being generous.
Please look after yourself, he's not a keeper.