I'm 43 and I can't learn to drive!! Feel useless

Are you saying that other parents who can’t drive or afford to run a car are failing their children? That’s really quite an unpleasant sentiment.

You are beating yourself up over something that your brain, probably due to combination of spatial awareness, executive function, anxiety, really struggles to do.
This doesn't make you thick, just that your brain may work differently. I'm sure you have lots of other great skills.
Please don't tie up your self worth with just one skill. There are many people who don't drive, although it may not seem like it.
It maybe time to take a breather or accept driving is just not for you, you've given it so much, don't let it take over your life.

If you do want to perservere maybe medication for anxiety or hypnotherapy may help?

I also struggled to learn, swapped to an automatic and found a wonderful calm and chilled instructor who I felt completely comfortable with, still took my 5 attempts to pass my test.
How comfortable are you with your instructor? Having the right instructor is so important.
I also think going somewhere quiet, industrial estate or early morning weekend lesson when roads are very quiet, or simple routes may help build skills and confidence.
Whatever you decide good luck and please don't be too harsh on yourself, you arent thick and you are definitely giving it your all, your perseverance and determination are really admirable.

Lots of children don’t have a beach at their disposal. As a child I lived 60 miles from the closest beach so visits were few and far between.

I think you are getting so bogged down with the feeling of failure that it’s clouding everything else.

Years ago kids didn't go to the seaside much, especially if they lived inland. A week in a cheap caravan by the coast in the summer was the most that many people could afford. The kids grew up fine.

I do feel you are looking for obstacles now and focussing on the thing you want to do and maybe just can't, rather than being open to other solutions.

Could you possibly be depressed? I ask as you are feeling you aren't a good mother and that guilt is often a sign of depression.

This.
can you move?

Sorry you are actually saying that if you can't learn to drive you'd put your kids into care?!!!!

There are ALWAYS other options to driving. Can you move to somewhere with better public transport? Get taxis (surely not as expensive all the driving lessons you are taking). Hire someone to help you take your kids to school on the bus.

Make sure your eyesight is up to scratch. If you wear glasses, check that you don’t need a different prescription.

Not suitable because you can't drive? Don't be ridiculous!

Not as expensive as 4 hours of driving lessons a week!

Now you’re being ridiculous.

Do you think you’ve got stuck in a cycle OP? Like your brain is now convinced you can’t do it. I would maybe…
*try guided mediations on YouTube (you are a calm confident driver on repeat can help honestly!)
*find a new instructor and start a fresh. Don’t tell them your history.
*If you’ve passed your theory book a driving test so you’ve something to work towards.

your driving instructor saying everyone he teaches first time sounds a bit silly…I didn’t pass til my 3rd time due to nerves so just messed up silly things, by the 3rd time I was convinced I’d fail again and was so relaxed about it I passed easily. Don’t forget to breathe and drop your shoulders, it sounds so silly but it is so important to just relax, good luck x

Therefore you need to find a solution to getting your kids to school because learning to drive clearly isn't something that will happen quickly. Even if you get to the point of being test standard then there is a huge wait for tests, people are waiting months for them.

Continue learning but sink your energy into solving the practical issues around getting your kids to school, you might well have to look into moving.

Can you plan for a non driving life, move house for example?

This.
If your brain and body just don't work in that way it's better to accept that. That's far better than being on the road and driving so badly you aren't safe.

I was behind someone yesterday who almost reversed into me twice at the drive thru because she went into reverse instead of 1st. Then left 10 feet between her and the next car in front of her so I couldn't get to the window to pay. Then took roundabouts at odd lines that gave the wrong impression of which easy she was going (no indicators of course). Was too close to the kerb at times and then would veer at an angle to correct and ended up too close to the white lines. Doing 28 in a long stretch of 40 (I couldn't overtake). She really shouldn't have been on the road.

I also have friends who can't drive, they just accepted they couldn't and find ways to get around it.

Cars are pretty expensive to run, I run a relatively cheap one, but it's still £300 a month all in including the loan, insurance and 1 tank of petrol per month.

I have often thought that, for that money I could just take taxis to where I need to go and cycle into town. I live semi rurally though so the car does win on convenience, just about.

Pethaps, but it is an option. Hypothetically, let’s say you went to the GP on Monday, and they diagnosed you with a condition which meant, legally, you could never drive. Would you reply that that wasn’t an option?

My husband is very very bright. He took 5 attempts to pass his test, and is a very poor driver. He us clumsy generally, and I think he may be dyspraxic. Nothing to do with intelligence.

Of course it’s an option. Anyone can be afflicted at any time with a condition that prevents them from operating heavy machinery, including a car. They don’t break the law and continue driving, they do something else. Now, it may be that you can learn to drive with enough practice, but it may also be that you can’t. Like any skill, driving is not something that literally every human being on the planet has the capacity to master. There is no getting around that fact.