I was on my own when my DC were similar ages. My thoughts are, right now life will be very expensive in terms of childcare and demands on your time out of childcare. That situation will ease over time with starting school etc.
Financially, not every pound is equal. The critical pound's are the ones that put food on the table a roof over your head, provide fuel and clothes. Subsequent pounds then make life nicer, more comfortable.
What are your wants in the more comfortable, you mention an old banger, travel, days out.
When my DC were little I ebayed everything not bolted down. If a toy stopped being used or clothes were outgrown, I cleaned them up and got them listed - often small bundles aiming for £5+ a transaction to reduce effort. I started buying good quality second hand clothes and toys for our use, then selling them on too. It was cost neutral - sometimes we even made a bit on purchase price.
We didn't do foreign travel until I remarried when they were a few years older. We did UK travel, just me and them though. I discovered Barcello hotels at the time had an offer where children stay and dine for free. A single room in Blackpool on the sea front 4* DBB was £69 - we were upgraded to a family suite for no extra charge. We had an early evening out seeing the illuminations which the DC loved and Tesco vouchers for attractions the next day.
We used to have lovely days down to London too. Great when the DC didn't have to pay train fairs.
Now we have a little more money and I'm married but we still try to make pounds go as far as possible. We've just booked regional flights to Hamburg in the school Christmas holidays £5.68 out for the DC (my cheapest find to date). We've upgraded and booked reserved seats got two nights hotel with breakfast for five of us for under £400. So £40/ night each with travel.
Last year we went to Berlin at Easter we paid £6 out each for the children.
Don't get too disheartened by right now. When they're so little it's just bloomin tough to make many changes. Time will pass and you'll gain more headspace as they become less demanding/ more able to play independantly. Drive is needed to help you succeed and feeling frustrated by right now shows that drive is there.