FaceTimimg Internationally

When you try to FaceTime her using her mobile number, do you include the same international prefix (probably "+1") that you would use if you telephoned her?

You should make sure the phone number you enter looks the same as one you would enter if you were to dial her for a telephone call.

Like sberman said, you need to include country code for all phone numbers outside your own phone number (or country). For example, a US number should start with +1 and continued with the (area code)-xxx -xxxx. Your other contacts which are probably mostly UK numbers do not need the +44 in the beginning because I guess the iPhone detects this with your own number and you wouldn't need one for all of them since you are assumed to be living in the UK. Also, make sure you guys do not have Do Not Disturb turned on. To check, see if there's a moon icon on top of your status bar next to the battery percentage indicator. If yes, turn it off by sliding from the bottom to access Control Center and turning off the moon icon (this is for convenience but you may also turn it off through Settings).

Hope it helps!