I think you can appeal and/or take it to HR. Have you explored the reasons for declining
I would go to HR as they should try and sort a job share rather than deny your application without a reasonable other option...
Could you use some AL 2 days a week until you can find something else or sort out alternative childcare or a job share
Could they move you to an area that could accept it?
I had to find another job x
I’m so sorry you are going through this- so frustrating