This isn't being caused by your iCloud account. It's being caused by using the same Apple ID for iMessage and FaceTime on both phones. To fix this, one of you needs to change to a different Apple ID for these services. (You can continue to use the same ID for purchasing from the iTunes and App stores.)
On one of the phones, go to Settings>Messages>Send & Receive, tap the ID, sign out, then sign back in with a different ID. Then do the same thing in Settings>FaceTime.