Well hopefully the OP will come back and clarify. But to answer the basic question, other people are 'surviving' (well not everyone is, but those are the ones that you can't see going on holiday or driving nice cars) because they're not paying such high rent and high commuting costs.
OP, you seem very unaware of what is normal/typical/average. You say you 'don't live in an expensive place' but your rent is £2k+ pm, which is really high.
And yet your DP has high commuting costs on top. People normally do one or the other. The ideal would be to live close to work so commuting is cheap and quick, but obviously many people can't afford to do that, so they live somewhere cheaper and suck up the commute. But not both.
I know you didn't ask for advice, but 'just having a moan' won't solve your issues, so you could improve your situation by:
Looking at moving somewhere where the cost of rent and commuting is much less. You say you'll 'never be able to afford to buy' but with your DP being a high earner, and when you go back to work, of course you will, so you'll probably benefit from renting somewhere smaller and cheaper so you can save a deposit - your bills will probably be lower too, so free up more for other things.
Why is he spending £300 pm on petrol, if he's travelling for work, his work should be paying for this, preferably at 45 ppm, so he gets a contribution towards all his car running costs. What's the car situation btw? Does he own it outright, or does he have monthly car payments?
£450 pm on groceries and nappies etc is quite a lot, so could you trim this a bit?
How much are you spending on things like phones, broadband, streaming, other subscriptions, there's loads of ways to reduce this if you're paying more than the minimum.
You need to keep your savings, like you say, they get used on annual and irregular costs like car repairs.
On the matter of work, you need to change your mindset over this. You're currently missing out on pension contributions while your DP is working and building up a good pension that you have no entitlement to as you're not married, so you're really at a disadvantage. So you need to change this by getting married, which doesn't need to be expensive, just go to the registry office. Also think about how you can work, and share childcare costs, and responsibility for childcare drop offs or work when DP can look after DC. Are you at least getting the NI credits towards your state pension, even though DP earns too much to receive CB?
But one thing you could do even if you don't work is keep a really tight rein on your budget, to make your money go as far as possible. Have a look at Moneysaving Expert as there's loads of ideas on how to increase your disposable income by cutting costs, and earning little bits of extra money here and there.