The correct way should have been to have the custodian split the distribution and have issued each person a 1099-R reflecting their portion. But now it is too late to get that corrected.
If the sister reported 1/2 the distribution AND 1/2 the withholding then her return will be audited so she should expect an IRS letter for the incorrect procedure.
Since this was all reported in your wife's SS# then it should all be reported on her return. To find out how much the other sister's half cost you in taxes is simple ... just enter 1/2 the distribution and look at the tax liability and then add the total distribution and look at the tax liability again. The difference would be the part the sister owes to you ... so let's say the total distribution was $20K ... and the tax with $10K on the return is $500 and with $20K it is $800 then the $300 difference is what the sister owes. So a check for $10K - $300 should have been issued.
So what your wife should do is what I described in the last paragraph ... put the entire distribution on your return along with any withholding. And the sister really should amend the return before the IRS catches the error.
