You will need to start from scratch, the content bought with your mom's Apple ID will always be hers, it cannot be transered to another Apple ID.
Follow these instructions so that you can set up an Apple ID that does not require a bank card for free content. You can ad iTunes gift cards or a bank card to the account later if you need to buy something;
Creating an iTunes Store, App Store, iBookstore, and Mac App Store account without a credit card -
You have to start from scratch. You cannot transfer purchases fro one Apple ID to another ID. Purchases are always tied to the ID that was used to make the purchases.
That doesn't mean that you can't still use the purchases - because you can. However, of you want to update any apps that are tied to your mom's account, you will always have to use her ID and password in order to update them.
If you want to create your own Apple ID, you need to sign out of your mom's ID in Settings>iTunes and App Stores>Apple ID. Tap the ID and sign out. Then you can create the new ID. Read more here.
Be aware of the pitfall of using another ID in order to download past purchases when switching ID's. Read more here.
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