@darknesspker: She is the princess's personal maid, in a way an 'accessory' to the princess herself, so I highly doubt they'd make her to such menial tasks that'd cause such scars to reduce her beauty.
Even the errand we saw in the 1st chapter was just shopping.
@Mrfishy: Maybe her little crush on him will make her take his stories of what's life at the bottom is like more seriously.
If anything he seem like a good candidate to get her to realize how privileged she's been.
Meanwhile Wang Mu's case seem like there's a lot of options to go for depending on how he think of the situation of Ye Hwa and Baek Cheon.
If he doesn't realize this 'Ye Hwa' is not the same, maybe he'll flirt with her and the misunderstandings pile up until the house of cards fell down.
If he does but misunderstanding the truth as the 'Ye Hwa' he met was actually 'Baek Cheon' pretending to be her own maid to go out incognito, he still have the problem of courting a princess WHO'S ON HER WAY TO GET MARRIED.
If he does, and guessed the truth perfectly, then aside from the whole she's about to get married, he'll have the perfect material to blackmail 'Baek Cheon' into going along with him...wait that sounds really fucked up.
Random thought: What if the mother actually gave birth to TWIN (making the two actually sisters), but since twins are seen as ominous signs, she have the maid took one of them away before people think too much on that.