Does a wife have the right to change her mind about forgiving her husband, and what is the Islamic ruling on that?

Residing in non-Muslim countries is forbidden except out of necessity, due to the harms that result from it. Therefore, we advise you to emigrate to a Muslim country where you can take care of your family.

As for your problem with your wife: if she is committed to religious rituals, then strive to reconcile with her, even with money. If she accepts, then praise be to Allah; but if she insists on her stance, she is disobedient. And if she insists on expelling you by exploiting man-made law, then there is no good in her, and it is better to leave her.