If she was patently "not mad" - which I understand to mean that no reasonable medical or lay person at the time would consider your hypothetical wife insane - then you're clearly referring to committal by conspiracy. The question itself covers a long time-span and is non-specific in regard to jurisdiction but the short answer is that it was possible, undoubtedly happened, but was by no means typical of committal practices. This is not to deny that a significant minority of male and female patients were committed during the 19th and 20th centuries for moral or other reasons that might seem dubious from a contemporary perspective but that does not necessarily imply committal by conspiracy.

Just to clear up some misconceptions that might be underlying the question, it can be said as a generality (very broad brush) that for most of the period covered by your question, the rate of female committal to asylums was not significantly greater than that of men (and in many instances men were committed at higher rates); that most admissions were for periods of less than 12 months; that unmarried people were committed at a significantly higher rate than married people; and that, without engaging in retrospective diagnosis, most people committed were evidently operating under significant emotional or mental strain. Typically families instigated committal procedures and the most important factor leading to committal and the willingness to receive a discharged patient was a family’s capacity or willingness to provide care. Family relations, emotional bonds, concerns about property or propriety were obviously important to such decisions but that is not to imply that a context of madness/insanity (as understood at the time) was absent.

This is not to deny, however, that gender, race and class were not significant factors in asylum committal, diagnosis, treatment and discharge. Historically contingent gender conceptions certainly significantly informed views regarding female mental illness.

Depending on the time, place, existing legislation and whether the asylum/mental hospital was a private, public, or charitable institution committal might have involved an application directly to the management board of the institution, to its medical superintendent, a judicial procedure, an application to local government/poor law officials, or, essentially, at a later period, an entirely medicalised process.

Most jurisdictions from the second-half of the 19th century would have minimally required some form of medical certification for committal. In England and Wales, due to fears about false committal (typically related to fears about property seizure; there was nothing like the same fears around false committal for pauper lunatics) medical certification for paying patients to private madhouses was introduced in the late 18th century (1774) and this was extended to public asylums during the nineteenth century when, or relatively shortly after, national asylum systems were established in most western countries. Certifying doctors, who were typically not asylum medical officers, might interview patients for committal, their family members and friends, and perhaps other members of the community (police, etc).

So, you’d either have to engage in some ‘gaslighting’ to introduce an appropriate context and produce symptoms of mental morbidity in your would-be wife, recruit the certifying doctor to your conspiracy, or rely upon the fact that the doctor would either be desultory in his/her examination of the patient (which certainly happened) and/or would take your or your family’s word regarding their mental state. If that was sufficient to secure a committal the medical officers of the asylum might still record that the patient was in fact sane which would likely expedite their discharge (although this could be mediated by your social status and the kind of fuss you, your family or other members of the community might kick up about her prospective discharge).

There are certain kinds of false information that might have made such a committal easier – claims that she had attempted suicide, sexual impropriety, that she was spending money excessively/inappropriately, etc – but normally such claims would have required some level of substantiation.

There's a ton of literature on gender and asylum committal; some of the earlier empirical claims re committal rates by some feminist historians have been rebutted.

Two useful sources might be:

Wright, David. “Delusions of Gender?: Lay Identification and Clinical Diagnosis of Insanity in Victorian England.” In Sex and Seclusion, Class and Custody: Perspectives on Gender and Class in the History of British and Irish Psychiatry, edited by Jonathan Andrews and Anne Digby, 149–76. Amsterdam: Rodopi, 2004.

Busfield, Joan. “The Female Malady? Men, Women and Madness in Nineteenth Century Britain.” Sociology 28, no. 1 (February 1, 1994): 259–77. doi:10.1177/0038038594028001016.