When you got a job, that also triggered a Qualifying life event for your spouse. A qualifying life event triggers a new open season window where you can make changes.
A change in your life that can make you eligible for a Special
Enrollment Period to enroll in health coverage. Examples of qualifying
life events are moving to a new state, certain changes in your income,
and changes in your family size (for example, if you marry, divorce,
or have a baby) and gaining membership in a federally recognized tribe
or status as an Alaska Native Claims Settlement Act (ANCSA)
Check with you wife's employer to see if you are still in the window to cancel her insurance. There may have even been two events: getting the job, and getting the insurance.
Here are more detailed examples.
Most people pick their insurance options when they start a new job or during the annual open season. Your complication is that those two events are either close together, or they overlap.
Lets say that a single person has insurance; and so does the person they are dating. The in the middle of the year they get married. The government calls the wedding a qualifying life event. They can decide during that window to merge plans. They can even decide to go from a plan with no dental to one with dental, or can pick the one with maternity coverage.
Now lets say that the person who has the family policy loses their job. Of course they would want to switch; and they can because loss of a job is a qualifying life event.
Now when that person is hired into a new job, they can decide to switch again.
The list of events that are considered a qualifying life event is long: marriage, divorce, birth, death, adoption, job change, eligibility change, age, retirement...
And if it is an event that impact one spouse, it also impacts the other.
Complication due to both spouses working
When both spouses work and are eligible for insurance, the two employers want to coordinate benefits. They feel that if the other employer doesn't have to cover their employee it is unfair. Some require that the other spouse must get coverage from their employer, or they charge a higher rate.
When both parents have family coverage they generally use the birthday rule to determine which is primary and which is secondary.
These are separate issues from Qualifying life events and open season.