Given my wife is putting down "homemaker" as her occupation, would we qualify for dependent care expenses? Or only if she actually earned wages? Is there a certain amount she would have needed to have worked earning wages or earned to qualify for deduction for dependent care expenses?
No.
Homemaker would be considered as her "occupation" but not as employed for any tax credits.
She would need to be employed or work as a self-employed taxpayer as a "Housekeeper" for clients, and her own family would not qualify as clients.
The Child and Dependent Care credit is only for the expenses you (and your spouse) pay someone else in order for you both to work, find work, or attend school. The "Care Provider" cannot be your spouse.