She can claim possible if all requirements are met but you cannot file a joint return with your spouse so the overall tax will probably be a loosing situation. All she can get is the $500" other dependent" credit (or medical expenses if she can itemize - unlikely) but you loose a $12,200 deduction.
---Tests to be a Qualifying Relative (& Unrelated Persons)---
(Must meet ALL of these tests to be a dependent)
1. The person cannot be your qualifying child or the qualifying child of any other taxpayer.
2. The person either must be related to you, or must live with you all year (all 365 days - There are exceptions for temporary absences such as school, illness, business, vacation, military service) as a member of your household.
3. The person's gross income for the year must be less than $4,300 (tax-exempt income, such as certain social security benefits, is not included in gross income)
4. You must provide more than half of the person's total support** for the year.
5. The person is not filing a joint return.
In any case, the person must be a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico
The above is simplified; see IRS Publication 501 for full information.
** Pub 501 Worksheet 2 for determining support
you and your spouse have the right to file a joint return if you both agree to it despite what her mother has done. you'll have to mail it in because your wife's SSN can be used on only one filed return in a year.