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The UK government recognises dual nationality and therefore obtaining a UAE nationality alongside your British citizenship isn't a problem. The problem your wife faces is meeting the requirements for obtaining a UAE citizenship, which implies that she will have to renounce her British citizenship. Unfortunately in this situation I say for lack of a better expression you can't have your cake and eat it. She will have to make a decision which citizenship is more important to her. If she decided to give up her British citizenship it will only affect her and not any other members of her family. But once given up, her rights to live in the UK will be affected and it is also very difficult to obtain British citizenship these days. There is also no guarantee that she will be granted a UAE citizenship.
I was only going by the information you provided that "Recently my wife has been given the opportunity to acquire her UAE citizenship"
It is a relevant fact if your wife was born a UAE citizen this is quite different from acquiring a UAE citizenship. If your wife has been advised that only when she receives a UAE citizen then she can renounce her British citizenship this is also a relevant fact missing from your initial question. If this is what she has been advised then the worry of being caught in-between the two processes does not arise. However, there is also the problem of renouncing her British citizenship.
Once a person has obtained British citizenship and then decides to renounce it, there is no provision under the UK Immigration Rules to directly apply for ILR.
If she wishes to live and work in the UK after renunciation, she will need to make a family-based application as a partner of a British citizen settled in the UK and go through the whole process again and meet the necessary requirements under Appendix FM. After 5 years, she would be eligible to apply for ILR. Obviously questions will be asked about her renunciation and she will need to meet the requirements at the time of application.
In theory it is possible to renounce a British citizenship but you must then return your British passport and inform the HMPO (Her Majesty's Passport Office) of your renounciation and then apply for a certificate of entitlement in a valid foreign passport.
Foreign passports which are being submitted for an application made in the UK must have have immigration stamps showing that the holder is resident in the UK. There is also no guarantee that an application for a certificate of entitlement will be granted. Before you make any decisions you must first seek legal advice as we cannot give advice on JustAnswer but only general support and information which must not be relied upon.
I have had sight of the attachment. My answers remain valid. If you have been advised to renouce your British citizenship as a condition of obtaining UAE citizenship to do otherwise would be seen as attempting to circumvert the condition of obtaining a UAE citizenship.