Can I move out of my parents' home while still asking them for school pickups?

Mum asked what time I'd be home. I said I hadn't decided. She replied, "Then I can't decide when we're eating." My first thought was that paying board should have bought me more independence. My second was that she was currently cooking for my child.

I've lived with my parents since a separation. I pay $350 a month and help with household jobs. They collect my seven-year-old from school twice a week when I work late. We have different expectations about meals, visitors and how much notice I should give when plans change.

A small rental nearby would cost $1,400 a month. In my working budget I can cover that and the normal bills, but it would leave much less room for extras. I would still need those two school pickups unless I arranged and paid for another option. I haven't asked whether my parents would want to continue them after I move.

How do I discuss the move without presenting independence as something they are withholding, or childcare as help they automatically owe me? I think separate homes could improve the relationship. I need to know what arrangement would actually make them separate.