How do they manage?
With extreme difficulty.
Here is my advise - think differently. You will have this issue for a defined period of time - it will ease when the babies are out of care and in school, when your trainingfinishes and so on.
You have to get a new flat so look ONLY where there are good non fee paying school options. That may mean paying a little more for rent now but you off set school fees and you "save". We did that - it really helped. We have school fees now but having them in state primary really hepled us save like mad and get organized.
"Save" for now by not running up debt or at least, really containing it. Be very strict with your budget etc. All children are expensive but the first is the most as you get all the kit for them. You should now only buy once as all can be passed down - so cost per wear of all clothes is really low in the end. When they grow up and get notions that goes out the window BUT you can have a good run.
Usual things then - like a carefully managed credit card for flight points etc. House swops are great for time away and people with young families really love them as the set up helps. We had some great trips that way - the cc points and house swops.
Something to keep your spirit up is the idea of saving the childcare money once the start going to school. You have no realy chnage in lifestyle but it starts to acrue very quickly.
Once you have finished traing you may decide to move where you will make significant savings.
The big ticket items are the care, the rent and in 4/5 years - school. Watch those and you will muddle through.
Good luck. Most of us get through it. You will too but it is scary.