I don't see that there's much you can/should do regarding your wife's sister at this stage. She has presumably overstayed the conditions of her visa already (tourist presumably), so this is now a matter for the DoJ to pursue.
Regarding the separation/divorce from your wife, you really need to see a Family law solicitor as the failure of one party to sign the separation documents is nothing new.
Regarding your wife's right to apply for Irish citizenship on the basis of her Marriage to an Irish citizen: she may only apply on these grounds if the marriage is subsisting at the time of application and that you are still living as husband and wife. If you read the info at the following
DoJ Site:
Naturalisation of spouses of Irish citizens
If you are married to an Irish citizen and living in the island of Ireland, you may meet special conditions for naturalisation based on that marriage if:
- • You are of full age (i.e. eighteen years or older, or married if younger than eighteen).
• You are of good character.
• You are married to your Irish citizen spouse for a period of not less than 3 years.
• Your marriage is recognised under the laws of the State as subsisting.
• You and your Irish citizen spouse are living together as husband and wife and your Irish spouse submits to the Minister an affidavit in the prescribed form to that effect.
• You have had immediately before the date of the application a period of one year’s continuous residence in the island of Ireland, and
• You have had, during the 4 years immediately preceding that period, a total residence in the island of Ireland amounting to 2 years.
• You intend in good faith to continue to reside in the island of Ireland after naturalisation and
• You make a declaration of fidelity to the nation and loyalty to the State (see below for the point in the process at which this is required).
The Minister for Justice, Equality and Law Reform has power (in his or her absolute discretion) to waive one or more of the conditions outlined above in the case of a non - national spouse of an Irish citizen applying for naturalisation if satisfied that the applicant would suffer serious consequences in respect of his or her bodily integrity or liberty if not granted Irish citizenship.
If you are separated then your marriage would not be considered to be subsisting. There is a clause at the end that states that the Minister has the right to waive any of the conditions if they fear that the applicant would suffer "serious consequence in respect of her bodily integrity or liberty if not granted Irish citizenship" but I've no idea how one can prove such a thing (unless as a refugee applicant would).
As JAJ suggested, you should not sign any document saying that the marriage is subsisting if it is not.
