Was the 'her' a typo? Did you mean 'here'? The difference between 'would' and 'could' is the degree of certainty. 'Could' is a suggestion. 'Would' is much more definite, and expresses a definite preference for that option. That sentence is a little odd, but it suggests that the person saying it is perhaps in some authority, like your boss, or perhaps your parent. The reason it is a little strange is that 'would' is a little forceful, but 'if you don't mind' is asking for your permission. It could even (depending on the tone, if it was spoken) be used mockingly.

Her = she, here=in this place