Inherited means someone died and someone else is the beneficiary and inherits the account. Inherited accounts have different provisions than when it is your own. Her mother opening it for her is a courtesy; not meaningful otherwise.

"The 1099-R does not provide basis and neither mom nor daughter Know about the basis other than what was put in originally."

That's no excuse. Any account statement will show new contributions and other withdrawals/distributions, as well as earnings.1099-R in prior years shows distributions. Form 5498 for any year with activity (contributions and distributions) will show the details, as well. If she doesn't have paper records, and can't log in to get them electronically, then she makes a request to the broker and agent holding that account. I've gotten 15 1099's for/with one person, this year, by doing this. Since 2011, brokerages maintain all basis in investments.

There are Three Roth 5-year rules:

https://www.investopedia.com/ask/answers/05/waitingperiodroth.asp

It's not just penalty. Doing this wrong can result in paying tax on her own already-taxed basis funds.