That's absolutely what is happening here. Mother is secretly running credit reports! They wouldn't usually know the amount in the account unless it's a credit account of some sort, which means that Mom is probably using some social engineering tricks once she knows the location of the account (she might even have the account numbers from the credit report, or some portion of the account numbers).

The key here is not just to close the account and transfer the money. OP must also but a "security freeze" on he credit report. I believe this must be done individually with each credit report bureau (Transunion, Experian, and Equifax). Once that's done, however, OP will need to provide a PIN number to authorize a credit report release any time one is requested. That should put the kibosh on Mom's meddling. Couple that with specific security freezes (require verbal pin when attempting to get any account access, for example) at whatever bank she is using and she'll have some reasonable assurance of privacy.

The last thing is to make sure she isn't being bugged. Could Mom have installed a keystroke logger to find out electronic passwords? Could she be somehow tampering with the phone? Paranoia isn't bad if someone is actually after you! OP should have her devices checked for nefarious intent as soon as possible.