The sentence doesn't really make sense, but I think you probably mean:
The news seems to have turned the heads of the two eldest daughters
The news is likely to have turned the heads of the two eldest daughters
The meaning of "turned the heads of" depends upon the wider context, but might mean either:
"caught the attention of"
"unsettled the minds of"
News of the planned concert caught the attention to the two oldest daughters - it would be a chance for them to show off their new dresses.
News of Fred's unexpected marriage to Jane unsettled the minds of the two oldest daughters - would they be the last of their friends to get married; maybe they'd never be married at all?