You're not useless, but your circumstances are working against you.
Frontline emergency services aren't paid very much for what they do and pay has stagnated over last few years compared with CoL.
You only work 12 hours pw (not a criticism, merely stating facts)
It's difficult to work around a shift worker without needing childcare - anyone saying WFH while the kids are there aren't being realistic. No employer will allow this unless they're secondary age, or possibly older primary for a couple of hours a day (eg after school but not all the time)
You have 3 DC which adds to the cost of food, hot water for baths, showers, laundry, clothes, holidays etc, everything costs more than for families with 1 or 2 DC.
You live rurally so need to run two cars and are limited in what is available locally, although it is good that you can shop at Lidl, which is likely to be significantly cheaper than if you had to use Tesco/Morrisons.
All the above adds up to below average disposable income which is likely to have got worse over the last couple of years to the extent that you're now really struggling.
Don't compare yourself to other people with different circumstances, as well as them possibly earning more or having lower costs, there's other unseen factors like debt, inheritence or help from relatives - sometimes grandparents give money or pay for things like holidays.
However, have you checked if you're entitled to help with the cost of childcare? I would have thought that you are.
Also, can your DH pick up any extra shifts, bank work etc?
One thing to look at is a really thorough review of your finances. If you can find a bit of extra income and trim a few costs, it might free up a bit of spare money to make things a bit easier. Have a look at Moneysaving expert, and also get the weekly email for ongoing tips on making the most of your money.
Eg, for family days out etc, your DH can join various public sector 'clubs' which give things like memberships that will allow free entry to attractions, so you can take DC out without it costing anything - take a picnic of course.
https://www.moneysavingexpert.com/family/money-help/