How do I prevent another receiver from stopping a show I am recording?

What DVR/Receiver model numbers do you have?

Which one is your mom's?

Yes, get a band stop filer to remove that receiver from Whole Home.

HOWEVER, if your mother has a Genie client, there is no way to prevent this as the Genie clients rely on the Genie HD DVR.

Hello there! I'll be more than happy to assist you with this and provide the best options available. I know how important it is for you to be able to record your favorite shows without any interruptions. I will send you a DM, so we can review this together. Efren, DIRECTV Community Specialist

Please try the steps below.

In this case you need to stop sharing with the other devices at home the playlist of your recorded shows. 

Press MENU button

Select "Settings," press SELECT

Select "Whole-Home," press SELECT 

Choose "Share Playlist"

Select  "No", press SELECT.

Efren, DIRECTV Community Specialist

Sounds like not a receiver, but a Mini Genie Client. The difference is that Clients are extensions of the main Genie receiver so have full access. Think of it as those TVs are all off one box.

If both boxes are actually receivers, then Menu > Settings > Whole Home > set Allow Remote Deletion to "NO" so that she cannot delete a recording (even in progress).