Thank you guys for your help.
I am wondering in case of appeal rejected what other option does my wife has? Because refusal notice states that she should make arrangements to leave UK if unsuccessful. How long the appeal decision take?

1st of all there is no need of being panic from the standard refusal letter because your non-EU wife still has the right of residence because only her PR confirmation is refused. You can appeal/reapply with correct documents covering 5 years of treaty rights evidences. Or your wife can apply ...

Me and my wife been married for over 9 years having 6yr old daughter and son due in 3 months. I am a EU member and my wife is non EU country. Until now she was on extended 5 yr visa depending on my status as a EEA sponsor. Over a year ago (yes HO kept us uninformed for over 12months) my wife applied ...