Your mother can file her own tax return, whether or not you claim her as a dependent. Claiming her as a dependent does not prevent her from filing her own tax return.
If she does file a tax return, she cannot claim an exemption for herself. She must indicate on her tax return that someone can claim her as a dependent. The question on the tax return is different from the question on the insurance application. The question on the tax return is whether someone CAN claim her as a dependent. Since you CAN claim her, she must indicate on her tax return that someone can claim her.
So she can file a tax return whether you claim her or not. And her tax return will be the same whether you claim her or not, since you CAN claim her.
