What is the ruling on keeping dogs at home if the wife is not Muslim and is unwilling to give up her dog?

The woman of thecriptures whom a Muslim marries must be chaste and the marriage contract must be religiously sound and complete in all its pillars.

Regarding the dog, you should try to convince her to give it up. If she insists, do not allow it into your house. In that case, there is no sin upon you.