Firstly, hardly anybody can actually afford a new car. 90% of them are financed, and to the point where the Bank of England has been warning of a credit bubble in car finance for some time. If you earn 50k, you take home 37k before any allowances or deductions. That's approximately the price of a new BMW 420d M-Sport twatmobile, sans optional extras. If you saved 10% of a 50k salary for a whole decade, you could buy one outright. Whoopie. One day out of every fortnight for a whole 10 years spent grafting for a boring diesel car nobody looks twice at that's worth nothing again 10-15 years later. Really? Bit daft? So why aspire to have one, or finance one for perhaps 20% of the fruits of your endeavours?
With modern consumer info and the choice and longevity in 2nd hand ones, new cars are a huge waste of money. I don't say this because I cannot afford one - my wholly owned business made over £100,000 profit last year, and I lived on rather less than half, so I could buy a new BMW twatmobile tomorrow, cash. My own daily driver is now 8 years old and I have no desire to change it. Boris Johnson certainly isn't short of a bob or two & drives a couple of ancient old bangers - I used to, but I cracked and bought a nice 5 year old car 3 years ago... but now I will keep it as long as it works.
Secondly, expensive topical holidays aren't all they are cracked up to be. When I first started making strong money, we went to an expensive & exclusive beach resort in the Caribbean.
We were both bored after 2-3 days, and were soon off on a cheap rented motorcycle and eating out at the little "no frills but great food" kind of places. I learned the expensive way that lying on a private beach or by an artfully landscaped pool with rich people waiting to down a few perfectly crafted Mojitos at a socially acceptable time, is no less mind numbingly dull than lying on a sun lounger in a cheap hotel in the med with a pint of Stella. In fact, it's a lot worse, because the kind of people you meet at a cheap resort in the med are invariably friendlier & more fun.
So, my first piece of advice would be for BOTH of you to actually think rationally about what you want out of life, and why? Where do you want to go, what do you want to see & do? What do you aspire to do with the kids? You can often travel to amazing places for comparatively very little. You can drive a cheap heap of a car to make those things happen, and if the trade off for driving a shitty old car is seeing the Taj Mahal, Golden Gate Bridge, or Machu Pichu, then frankly, give me the old banger. I know that isn't for everybody, but you can have a nicer car and a lot of fun out in the British or French countryside camping for tuppence ha'penny. I had a wonderful time camping in Wales a few weeks ago. Live life, be grateful for your health and to live in times of peace and relative plenty - it's not a rehersal.
Secondly, yes - you should be open to earning more, whether F/T or P/T. Relationships are a compromise & you're not doing that much on the work/wage front and it sounds like you never have. Stressful life for him, charmed one for you is how the story plays to me. If you aren't both happy it's clearly unfair. It's not about bringing equal £, but about making equal sacrifices. If you brought home £12k instead of £8k, you could take your kids on an amazing couple of weeks away in a completely foreign culture every year without any impact to your other financial commitments - think about that?
Lastly... 6 years goes by really fast. In 6 years your youngest can vote, drink & marry. What's keeping you together afterwards? (Refer back to point on what you both want out of life?). You can guarantee he's already wondering based on recent conversations. How far does half the joint assets & 8k a year get you? Things clearly aren't great, if you aren't thinking about how you'd support yourself as well as how you can lift some financial strain on the relationship, I think it might be prudent to do so - but if you thought more about exploring joint goals and aspirations & making them happen... maybe you'd need to worry less anyway?
PS... I appreciate my statements about being well off but not enjoying spunking money may sound a bit self-righteous & I think in some ways, you have to have money and spunk it away to understand it is pretty shallow. However, that also makes you appreciate what you had to do to get it, and a partner not really pulling their weight in effort terms if not outright financially can lead to resentment (been there too).