Hey there, Riley!
Thanks for stopping by the Apple Support Communities. I see that your mom's new Apple Watch isn't vibrating as expected when on silent. I'm happy to help!
First, check out the information under the "Manage Haptic Alerts" section of Change the audio and notification settings on your Apple Watch - Apple Support. While I see you've already made sure it's on, your mom may want the "Prominent" setting, or need to adjust the way she wears the watch to create better contact with her skin.
If that doesn't resolve the issue for you, make sure Do Not Disturb and Theater Mode are not enabled by swiping up from the bottom of the watch display to access the Control Center.
If the issue continues after that, don't hesitate to respond back.
Cheers!