You are covered by a retirement plan at work. Whether or not you use it doesn't matter.
So your wife can contribute to a deductible IRA as long as your MAGI is under $184k since she is not covered by a retirement plan at work but her spouse is, and you can contribute to a deductible IRA only if your MAGI is under $98k.
Since you wife is self employed, she could open a solo 401k and have a potentially much larger limit (depending on income), but it has to be opened in the year you want to make contributions for, so it's too late for 2016. She could still open a SEP IRA and make contributions based on 2016 income. *Edit: This would mean she would have a retirement plan at work, so she would also be subject to the $98k limit on deductible IRA contributions (for the regular IRA, not the SEP).