This seems harsh - but, if it is a written policy of the bank, it appears your daughter doesn't have a choice. The only choice I would suggest is that she doesn't reopen a C D or any account with that particular bank! You daughter should ask to see the written policy re CDs.
Whoever your daughter talked to has no idea what she's talking about. Federal law says that upon death of the owner of a CD, the CD can be cashed in without any penalty. The bank cannot adopt a policy which overrides federal law.