Oh, the fun of struggling with a tween/teen who wants individuality! You have to find a balance between getting her to consider others' feelings and what her style may imply as disrespect (whether she intends it that way or not), and what squashing her personal style says about others being unnecessarily judgmental. You say she doesn't care what others think - but I think most kids really DO care and they're trying to find their own way.
I think it's helpful to try to put others' judgment of YOU aside if you can (I know that's hard especially with in-laws). Not sure why they would judge you more harshly than your husband - it's part of the old attitude of making the mother in charge of all things fashionable.
I'm not sure where you draw the line most of the time - you say her Goth look is okay if she does what you and her dad say in daily life. Does this mean that she obeys other rules and does chores, or do you regulate her "look" in her daily life as well? Sometimes making too big a deal out of a phase like hair and make-up makes a kid rebel even more, and trying to ignore it is a better tack.
Can you compromise? If she's already rebelling against frilly stuff, does she have to wear "spring colors" to the grandparents' house? Can she do something more toned down? Can you allow things like coloring the ends of the hair blue and some make-up, in exchange for not doing something more extreme? If her clothing is appropriately dressy for the occasion (no rips, no tears, no denim, whatever the rules are), maybe it does't need to be pastel or floral? Can she find a nice dark red or maroon instead of funereal black for the nails? What about the neutrals suggested below, maybe a skirt with leggings?
Then practice some responses if you do get criticism, like "She's exploring her style" or "The surest way to get a young teen to dig in her heels is to critique her publicly." Or "She spent a lot of time trying to look special - let's tell her we appreciate that she tried." Then change the subject. If Grandma wants to ruin the day and make your daughter hate coming over there by telling her that she looks like a tart or like death warmed over, she'll have to recognize that she's making the child miserable through criticism, at least as miserable as the child will be if she's wearing pastels. It's a trade off.