Well as Islam consider the husband-wife relationship as a very delicate matter, we always find the words "و ان خفتم" ="And if you fear that ..." in related Qur'an Verses.
Now let's take the legal (shari'a) part of the Issue:
- If your wife got married without being divorced or the khull'a has been declared and the specific 'Idah has passed, then her new marriage would be considered as invalid by any shari'a court!
- And of course you have the right not to give her divorce and she shouldn't ask for divorce/khullu' without a cause or harm because of the hadith narrated by Tawban (in Jami' at-Tirmdihi, sunan ibn Majah and sunan abi Dawod). So a reason for asking divorce for a wife could be that the husband doesn't care much for her, harm her or treat her badly or if she dislike him for some reasons (like his attitude, his weakness, his age etc.) as mentioned in the sahih Hadith about the wife of Thabit ibn Qays (in sahih al-Bukhari, sunan abi Dawod and sunan an-Nasa-i). And the later part of (2:229)
... But if you fear that they will not keep [within] the limits of Allah , then there is no blame upon either of them concerning that by which she ransoms herself. These are the limits of Allah , so do not transgress them. And whoever transgresses the limits of Allah - it is those who are the wrongdoers.
So if any of these reasons were the case the court could divorce her even if her husband was against that if this would be beneficial.
- On the other hand some scholars (apparently salafi in first place) point at the matter that a wife should obey her husband and if she didn't they would consider her as nashiz ناشز (so she should also share his bed if he wanted her to according to the well known hadith of abu Huraira which i have tried to explain here).
- But still it is recommended for both the seek people who could interfere as intermediators and try to solve the issue in a friendly and beneficial way!
- Again it's haram for the husband to keep his wife against her will or to cause harm to her (2:231)
... and do not keep them, intending harm, to transgress [against them]. And whoever does that has certainly wronged himself. And do not take the verses of Allah in jest....
... So do not incline completely [toward one] and leave another hanging. And if you amend [your affairs] and fear Allah - then indeed, Allah is ever Forgiving and Merciful.
and also (2:229)
... Then, either keep [her] in an acceptable manner or release [her] with good treatment ...
So you should try to find mediators who try to reconcile or clear things out, you should tell your wife that she can't get married unless she is really divorced! And that she would live in an invalid and therefore haram relationship! And as @Aboudi wrote in his comment you should consider giving her the divorce, because if she doesn't want to live with you any more, what is the use of staying married? Of course she could ask for khullu', which is much better for her then in the Jewish religion were (AFAIK) a woman can't get divorce that way. So you must think of it well because if you don't respect her decision you are sinning as you may be a cause of a haram relationship!
Read also my sources in Arabic: a primary salafi view on a woman who asked for divorce while her husband refused to give it to her and about a woman asking her husband for divorce.