If you are providing more than 50% of their living expenses, you may claim your children as dependents. If you and your wife are legally married, she is your spouse and you should file married filing jointly to get the best tax result. If you and your wife are not legally married, then you can claim her as a dependent also if she earned less than $4,050.
See SuperUser SweetieJean's answer below for more information:
https://ttlc.intuit.com/replies/4769507