Hey there takoyukii,
Thanks for reaching out to the Apple Support Communities.
To get started, since the notification appears on both you and your sister's Apple Watches when trying to send the invite, do you and your sister happen to share an Apple ID account? If so, then it is possible that may be the cause of the issue, and Apple does recommend that each person have their own Apple ID to avoid situations like this. Check out this link for more details: Make sure that each family member has a unique Apple ID - Apple Support
If you and your sister do not share an Apple ID account, have you had a chance to work through the steps in the following resource that can help with this specific issue: Use Walkie-Talkie on your Apple Watch - Apple Support
If you're having issues sending and receiving invitations
1. On your iPhone, open the Settings app, then tap FaceTime. Make sure that you're signed in with your Apple ID. Under You Can Be Reached By FaceTime At, make sure that your email address is selected.
2. Restart your Apple Watch.
3. Restart your iPhone.
4. Try to send the invitation again. On your Apple Watch, open the Walkie-Talkie app, swipe left on the contact, then tap the delete button 
. Tap the plus button 
, then choose the same contact.
If you still need help
If you updated to watchOS 5.3 or later and tried the steps above, but still need help, contact Apple Support.
If you've gone through the steps above, and you're still running into issues with sending an invite to your sister, the next best option may be to reach out to Apple Support using the 'contact Apple Support' link under the 'If you still need help' section above. You can also reach out direction at this link here: Apple Support
We hope that's able to help.
Have a great day!
