the tax laws say the parent that can claim them is the one with whom the children lived the greater portion of the year. this rule comes before the AGI rule. Assuming you are the one entitled to claim them under the rules above then:
all you can do is claim the children and paper file.
don't bother with attaching an explanation to the return it probably will be ignored.
you can file form 3949-A to report your spouse claiming false exemptions
https://www.irs.gov/pub/irs-pdf/f3949a.pdf
can't say the IRS will act on it because it is your spouse
if not, eventually each of you will get a notice asking to amend (remove the dependents)
if she doesn't then there will be a second notice to each asking for proof that they are the one entitled to claim the dependents.
your spouse will get a bill. if she doesn't pay the bill, then you can expect the IRS eventually to put a lean on any property she owns which may include and jointly owned property. you may want to consult a lawyer about this.
