DD dad and 1 aren't together. We have a casual agreement for who DD stays with and when (I.e not through court/ legally). She will stay with him around my work (could be 4 days one week or could be 2 days the next- I can be working from home/in office/away to meetings in other cities so very varied). We get along well and this arrangement has always worked.
It would make sense for her to go to a school in exDP area because due to my shifts I generally wouldn't be able to do the school run. He could take her any day and I probably could 2 days out of 5.
How does it work when applying to a school. He is on the birth certificate but all DD things (passport, doctors surgery, tax credits etc) are linked with my address.
We are in Scotland.