From the beginning:

My daughter needed a place to live and a friend said she could put her matress and belongings in an "alcove" of her one bedroom apartment. The verbal agreement was after two months she would pay an agreed to portion of the rent and that was all.

At the end of the lease on that apartment they agreed to find a two bedroom place. "Friend" signed lease (not my daughter) and the verbal agreement between friends was that my daughter would pay half the rent while working and going to school. Once my daughter got a job in her new profession she would then pay 50% of everything.

Two weeks after graduation my daughter moves out. She paid for the upcoming months rent so in essence gave 30 days notice. Now ex-roommate wants to sue her for money she claims is owed to her.

Does this sound like grounds for small claims court?

... She paid for the upcoming months rent so in essence gave 30 days notice. Now ex-roommate wants to sue her for money she claims is owed to her.

Does this sound like grounds for small claims court?

Not unless the ex-RM feels that the 30-day "in essence" notice wasn't sufficient under the law. Could be something there because:
Such notices

must be in writing and
have to say that renter (your daughter) will be terminating. You didn't say that it did.

I just told her she needs to send it to her in writing. Will send it with a return receipt request for proof. She has not proof of any other monies owed. Nothing was in writing so how could she and my daughter lived up to her end of the verbal agreement. Now she is getting bombarded with nasty texts.

Now you're cooking with gas.

Nasty texts simply suggests that she is upset. If your daughter has given her a 30-day written notice your daughter is probably in the clear.