What is the ruling on my remaining with my wife who apostatized from Islam and then returned to it, given my lack of trust in the sincerity of her repentance and my unwillingness to emigrate to her country?

It is advisable to be cautious when marrying someone who merely feigns Islam. If you marry her after she has pronounced the two Shahadas and outwardly committed to Islam, with a guardian and witnesses, then she is your wife. Her apostasy from Islam necessitates considering her a stranger, and if she repents during her 'iddah (waiting period), she reverts to being your wife. If her situation becomes upright after the two Shahadas, then consider her outward appearance. If you fear for your religion, do not travel to her; rather, try to bring her to you, otherwise, separation might be more appropriate. The idea that no woman would desire to marry you because you are divorced is far-fetched.