South African wife has Cyprus perm residence card live UK?

[worlddance]

Hi please can some shed some light on this for me as i want to find out where we stand in Europe.

OK so I am English 47yrs UK passport, My wife is South African 40yrs (south African Passport)
Currently we live in Cyprus where we got married last year.

My wife now holds a permanent residence card for CYPRUS AS A FAMILY MEMBER OF AN EU CITIZEN
Which by the way is not in the Shengen treaty and she still got this.

We are having a baby in Dec and soon after want to return back to the UK

SO..

As my wife has permanent residence card stating family member of an EU citizen.
Can we now fly to London arrive and show.
1. Our marriage certificate
2. Her South African passport which has now been changed with my Surname now.
3. Her Cyprus permanent residence card stating family member of an EU Citizen
4. Our daughter who has a British passport and British birth certificate.

I am told under the rules UK is in the EU will they accept her marriage to me and the fact she is already a holder of a permanent residence card for an EU country.

As she is traveling with me and our daughter ... will she be given entry into the UK or will she be turned way.

will they let her in and make her apply ?

Or is the CYPRUS PERMANENT RESIDENCE CARD ENOUGH NOW FOR HER TO BE GRANTED MY WIFE ...

Everywhere i read it seems everyone and the cat has different answers on this

Would really like to have everyones views on this matter as it seems eveywhere i go im told conflicting answers

thanks so much look forward to replies

[Casa]

If you have been 'exercising your Treaty rights' in Cyprus, through employment/self employment/self sufficiency (with conditions) you can use the Surinder Singh route to settlement.
Have a read through the information in this link:
https://www.gov.uk/family-permit/surinder-singh