No, the law does not allow it to be put back into a beneficiary IRA. Once a non-spouse beneficiary receives a distribution from an inherited IRA, it is forever distributed. This distribution received in 2017 is taxable on your 2017 tax return.
If you or your wife is eligible to make a deductible traditional IRA contribution, a new regular traditional IRA contribution could be made to reduce your taxable income, but this would have nothing to do with the distribution from the inherited IRA (other than subsidizing your new IRA contributions). It would not be a rollover.
