Hello emilia_,
Thank you for the details of the issue you are experiencing with FaceTime. It sounds like you have isolated the issue to your MacBook Pro.
You may be experiencing this issue due to an expired certificate that can be updated by running the software updates on your MacBook Pro. I recommend reviewing the following article:
Unable to make or receive FaceTime calls after April 16, 2014
http://support.apple.com/kb/TS5419
If your software is up to date, I recommend continuing to troubleshoot with the steps in the following article:
FaceTime for Mac: Troubleshooting FaceTime
http://support.apple.com/kb/TS4185
Thank you for using Apple Support Communities.
Best,
Sheila M.