I'm confused. A sim card is provided by your selected carrier for cell service, Apple does not issue sim cards. It also has no relation to the Apple ID used on the iPhone.
If you bought a new iPhone without a sim card, then you need to contact your chosen carrier for service and a sim card from them.
The Apple ID your mom used should have no relation to your dad's new iPhone.
Perhaps you can explain exactly what is going on, and what you cannot do.