Forced to Renew?

My new (and highly unagreeable) wife is a dependent to my visa and we must leave for home soon in order to renew our visas.

My question is whether I am forced to renew her visa as well as my own? Or can I simply choose not to renew hers?

It may sound cruel, and in fact I would love it if she were to divorce me on such grounds, but as it stands she has decided to make my life miserable while refusing to grant me a mutual divorce.

No one can force someone else to sponsor an immigration application. It is a voluntary act.
Likewise, applying for an immigration application is voluntary, not something that can be forced to be done.