This isn't the reality of the rest of your life. It feels overwhelming but your DC will grow up, will become more independent and you will have more time/ energy/ ability to focus on generating extra income.
With shopping do you go through your receipts? I used to once a month, looking for creep - branded DC yogurts/ drinks/ biscuits being key culprits. I also like to look at cost per meal as I found some meals I'd thought were not that expensive when I added up all the bits I'd get in for them were near takeaway prices. If you take out everything not essential how much do you save, then choose a percentage of the not essential as choice items in the knowledge those are choices. Then they feel more like treats.
I used to trapse round lots of supermarkets, rotating the one I shopped in each week, knowing the price in all of them to get the cheapest pasta/ pasata/ beans/ coffee. To an extent I still do. I download vouchers - farmfoods newsletter comes with vouchers and I think its £2 of £25 or £5 off a £50 spend - with butter at £1, milk 2 x 4ltr for £1.60 and squash was just on offer at 39p, 3 kg of pasta a couple of pounds. Its easy to do a bulk shop to get that £5 off and fill the shop with things cheaper that you could get elsewhere.
With earning potential, you do have lots of skills- you just haven't yet monetised them :-)
You juggle 4 DC and a house project whilst you have a DP who is working all hours - that is quite some skill.
I was technically below the poverty line when my eldest two were little and went through a phase of selling everything not bolted down. I got good at buying branded good condition items second hand for the DC at bottom market price, they had use of them then for the majority of items managed to sell for the same or more when the DC outgrew/ lost interest. So things became more of a neutral expense and they had nicer things rather than buying cheapest and disposing when done.
Have you checked the full benefits situation and if you can get any help with childcare should you want to go that way now or with wrap around in the future or potentially even just general living expenses now?
Do you think this money tightness is primarily tied to children being tiny if you can go interest only on the mortgage until they're school age?
I have this philosophy that when you're in tough times, not every pound is equal. When I remarried, DH's wage just about covered bills and a frugal lifestyle but any money I could bring in made life that bit nicer to live. So rather than putting the unrealistic expectation on myself to have a wage - I'd set myself a challenge for a thing we wanted/ needed. No pressure just like a mental image in my head of a thermometer for a fundraising campaign and each little bit I managed to generate worked towards that target. I tried all sorts of things from local pickup selling like facebook selling, etsy, eBay (which I have now evolved to do as a decent profitable business).
So you mention your flooring. Do you have something in mind you'd like to have? Have you costed it?
Have you looked on selling sites like eBay (who are actively promoting personalised items at present) and Etsy to see if potentially there could be a bit of earnings potential for some of your items? Its fairly low risk and low cost to give it a try.