Can my flexible working request be refused if health and safety comes into question?

[2Ees]

Apologies for the lengthy post.
I've made a request at work to reduce my hours due to stress/anxiety and also safety concerns. I have a 90minute - 2 hour commute to work to do a 12 hour shift and the times I finish (early hours of the morning) mean public transport is not available so my only option is to drive. On a few occasions I have fallen asleep at traffic lights so have been worried about this happening again and obviously it being a danger to myself or others on the road.
I stated this concern in my request as a reason for the change as well as the effect the job is having on my mental health. But was told the reason for rejecting was because the company is losing too many staff in the out of hours period.
My request was to work over the weekends Friday Saturday and Sunday ranging between 1pm -9pm and 3 days during the week 1pm-9pm. Instead of 3days 1200-0000 and 1900-0700 3days. I'm waiting to see if my 2nd request gets approved but fear it will be the same response as they want staff in the building overnight.
I also have 2 young daughters who I need to be home for in the mornings to get ready for school.
I'm struggling what to do as my next steps as if I can't reduce my hours to something safe I can't continue to work there.

Am I being unreasonable in my request?
Is this something I should raise with HR?

You work the overnight shift now and you want to switch to evenings?

moving off the night shift is just a common request that people have made for all of history. Submitting it as a flexible working request seems unusual and likely to be rejected.

I might instead rephrase it as a desire to be considered for another shift whenever a space opens up.

Thanks for all the responses, to answer a few of the questions, when I started the training it was different hours so the times I was travelling then were more during the off peak times so travel was only taking 1hr20 or less also the shifts were shorter, between 4-6 hours. So travel wasn't an issue. I do understand the commute isn't the companies problem but when I started I didn't know it would be an issue either. At the moment there aren't any staff but myself and 1 other I believe who does nights in office everyone else WFH so that's why they don't want to lose staff. Ultimately I do agree I probably will need to look for something closer that fits better with my schedule. But again thank you everyone for your responses