It depends.
The Grandmother's husband does not have to be related to the kids to deduct them if they live with him. They just have to fall into the "qualifying child or relative" rules. The IRS does not have the same definition of relative-it does not mean blood-related.
Since they live with him and the Grandmother and they are under the age of 19, he can claim them.
In order for you to claim them, they would need to be with you half the year or 183 overnights.
Child or Qualifying Relative:
Under the qualifying child rules:
Your qualifying dependent must live with you for more than half the year.
The qualifying dependent must be one of these:
Under age 19 at the end of the year and younger than you (or your spouse if married filing jointly)
Under age 24 at the end of the tax year and younger than you (or your spouse if married filing jointly)
Permanently and totally disabled