And if she files her own return, does this mean I can no longer claim her as my dependent?
Yes, she does need to file a return for Form 1099-S.
This list from the IRS includes the situations that require the filing of the form when received.
Generally, you are required to report a transaction that consists in whole or in part of the sale or exchange for money, indebtedness, property, or services of any present or future ownership interest in any of the following.
But you may be able to claim your mother if she meets the qualifying requirements to claim a parent.
From a TurboTax Help article:
Qualifying relative
When you add someone as a dependent, we'll ask a series of questions to make sure you can claim them. There may be other tax benefits you can get when you claim a dependent.