He's your brother so it's understandable that you're on his side but I think I would take pretty much everything he says with a pinch of salt.
£1200 for full time childcare seems pretty low. But okay, perhaps.
Putting that aside - ou think it only costs £300 or less per month for a one year old? What planet are you on?
For a start, she needs a two bedroom flat/house - no house shares or one room apartments. Which comes with additional rent but also more council tax, more heating, more gas etc etc etc.
Nappes, wipes, clothes, food etc etc et - relentless at this age.
What about any extras? if she wants a night out - what is the baby sitting cost? Around here, you're looking at minimum £11 per hour. MINIMUM. So either she doesn't spend the money but also never gets to go out.
He says he goes up when he can? What does that actually look like? Because I'm guessing it's not every week. And when he's there, is he ever taking the child over night? Or is it all at her house and if she's really lucky he takes the baby to the park for an hour?! So she gets no break ever unless she's able and willing to pay wifor it.
As for the £4500 per month... yeah, I think that his theory now hat she earns is as likely to be confused as the two of you are about the cost of childcare, rent, food, nappies, babysitters and more.
If he's genuinely paying more than the CMS amount then no, he doesn't have to give more money. But he needs to stop trying to pretend he's this great dad and man who is genuinely doing everything he can.