I read over your prior posts, and it looks like a year ago (plus), your 13 year old daughter was struggling with being a child (My Little Pony obsession) vs. a teen (allowance, Tumblr account). She was giving very clear signs of transitioning to full blown adolescence. This is completely normal.
Now she is rebelling. She is sneaking out with clothes you feel are inappropriate - and you may or may not be right about the clothing. It could be that her taste is extreme, or it could be that you are too strict. Either way, the most important things you should be focusing on are a) where did she get the clothes (friends?), b) where did she get the money to buy them (dig into this big time unless you know she has a lot of allowance money), c) what does she think clothes say about girls and who is she dressing for, and d) why do you have a daughter who hides these things from you?
I agree with the others below who say to stop wasting time and money on a home school uniform that is excessively conservative, and admit that you are closing the barn door after the horse has escaped. Shaming her into wearing something is the surest way to drive her further away from you and encourage more sneaking around. You should be looking at the causes of her actions, not coming up with some ineffective technique like regulating the jewelry and makeup she wears to home school. She's going to think you are completely out of touch and irrelevant. That is the last thing a mother should strive for in her teen.
Instead, you should find some appropriate compromises. You should work on the consequences for sneaking around and lying to you. You should emphasize that you want to trust her and know what she's doing and who she's with when she's out. You can start a school project on advertising and fashion images/messages about women: tiny sizes, cleavage-baring, butt-emphasizing messages that say girls and women don't feel good about their bodies and only dress and starve themselves to appear more sexual to men. But it can't be with the goal of getting her to wear a collared blouse and a knee-length skirt.
Dressing her like someone from the 1950s is going to alienate her entirely. She's going to be driven into the arms of someone who will take her away from all of this. Since you seem to be so far apart from her, I'd consider some family therapy to work this out if you can't do it alone.
Look at some teen magazines together - there are some great outfits with, say, short skirts but leggings underneath (practical in the winter and modest as well), jeans tucked into cute boots, etc. Look at girls in the public eye - the Obama girls are good examples of kids who want to be trendy and have lots of friends but who dress modestly. You want to avoid Miley Cyrus but you don't have to go so far the other way that you dress her like a boarding school girl from 50 years ago.
The general rule is, you give them some freedom in their clothing and hair - you can forbid bare bellies and printed messages about sex/drugs and anything written across the butt, sure. But some cute layers and trendy jewelry? Believe me, she knows a lot more about what's fashionable right now - get her to share it with you. You can draw the line at tattoos and piercings, but if she wants to dye her hair or put in a red strip or two, so what? It washes out!
Bottom line - if she can't express herself and experiment more in front of you, she's going to continue to hide and sneak, and do everything she can to get away from your rules. Find a middle ground. Fast.