Apple will absolutely insist upon a payment method being present in various situations. Since you are encountering one of those, one will have to be present.
If your mother uses Apple equipment too, the easiest solution will be for her to set up Family Sharing with Ask To Buy.
Set up Family Sharing - Apple Support
Approve what kids buy with Ask to Buy - Apple Support
If she does not, see if adding her payment method for this one purchase satisfies the requirement. The drawback is that if there is an ongoing subscription, it may then not let her remove her card until the subscription ends.
Note that you can still make the purchase with your own money as long as you have personal account balance by adding a gift card to your account. In most cases that will be used first before any attempt is made to charge your card, but the card may still have to be there. Sometimes it only needs to be there once.