We cannot give you legal advise here, but the IRS does not follow local court rules.
Basically, since you have her more than 6 months out of the year and you meet the criteria to claim them every year, as the IRS told you, you can claim them every year. From a tax perspective, her other grandmother cannot claim her since she does not meet any of the guidelines to claim her.
If her other grandmother claimed her this year and you did as well, whoever files later would end up needing to mail in their tax return and the IRS would use the Tie Breaker Rules to determine who gets to claim them. In the situation you are describing, you would be the one who would "win"
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