Flexible hours

Hi All, just need a bit feedback from you guys.

am registered mental health nurse in NHS. I have a son who is diagnosed of Autism age 8 years old. Am i eligible for flexible hours at my work place. The trust want me to work 5 days a week same for my wife , that mean we will have not enough time to spend with my son. we normally works 3 long days which allowed us to have more days off to support him. Since they have made this change , we as a parent we are very stressful about this change at tne moment.

Any advice please