You need to sort this out.
Even if you had been offered the schools you wanted close to your Mum's you would probably have been turned away because when you accept a place, and then start school, you have to give PROOF that the child lives at the adderess. So they will ask for a Council Tax bill in your name, or maybe the Child Benefit letter paid to you at that address. And they may do a home visit, too, to check.
Go back to your local authority admissions team, update you details to your own address and then ask to be put on waiting lists for the schools closest to your own home that you would like your child to go to. Or you can put your name on the waiting list for any school you would like your child to attend, including the ones near your Mum's.
However, waiting list places are given out accoding to the same admissions criteria, so you will have a better chance the closer a school is to your hosue, or one for which you are in catchment.
Unfortunately councils do not take the address of childcare arrangements into account.
just 'update' your addess details and apply (by going on the waiting lists) for schools close to you home.