No, my brother and his ex-girlfriend (the mother) do not live together.
My niece is 6.
My brother is named on her birth certificate so has equal parental rights and responsibilities but she lives with the mother so she is therefore primary carer.
If while my niece is with my brother, (one evening per week, every other w/e and by arrangement during school holidays) and he wants me to look after my niece, as she is in his care at the time, can he determine this under his equal parental rights although the mother has said she doesn't consent?
And if that happened and the mother then stopped my brother's access to his daughter, would she be acting illegally in stopping his agreed access?
Yes, I see my niece often enough when she's with my brother.
There has been no circumstance at all for her mother to now say that she doesn't consent to my taking care of my niece on occasion, she is simply being obtuse.
She has a history of making things as difficult as she can for my brother i.e. my not being able to look after my niece occasionally will be more awkward for him.