@silentscarlettt. I don't think they would let her enter in the Imperial Palace, since she was a commoner, and even if she could have seen him at least once it would be because he might be checking on the people's town and might of not hear her, that's mainly the problems
The rumors would increase even more since he's crown prince, because she was commoner, they might decide to make her a concubine, it's not bad being one but she wouldn't have any respect cause even now as duchess she has rumors about selling her body, nobody would believe her if she said she didn't sold her body.
And the castle is still a dangerous place, with people that decide to poison or kill her because she was a commoner, and the only way she might get some respect is by saying she's a purifier but that's not it..