If you are filing form 1040, Schedule H must be attached to your return. Since this must be attributed to one return it is not possible to allocate the tax liability from this filing through any filings with the IRS.
The only way that this can be resolved is if each of you filed Schedule H to divide the amount paid to the Nanny, thus splitting the tax burden. In this case the Nanny would be employed by two individuals and would receive Two Separate W-2s.
