Just one more add to what Anna and John have provided.
For your wife to be eligible for Medicare, it is two years as Anna said PLUS 5 months from the date of the determined disability (not necessarily the date used on the application). The 5 month addition is called the "Waiting Period". So if she was awarded SSDI effective January 1, 2015 then she would be eligible May 1, 2017 (it MAY be June 1, 2017 because of how they roll to the next month). It's the same way with the monetary benefits.
For what John said is correct but the rule is if the private insurer has less than 100 employees in total, it would be the secondary payer but if over 100 employees, the private insurer would be primary.
Also, IF you wife is awarded and at some point wants to return to work, make sure you follow the "Ticket to Work Program" program. Any attempt to go around that process could jeopardize her SSDI status.