Your 14 year old is caught in the middle. She's not the oldest, and she's not the youngest. Sometimes she'll want to be treated like she IS the oldest, and other times as if she's the youngest. And I suspect she's figured out how to pull mom's trigger . . . and then when it works, she rolls her eyes at you and you get even more frustrated.
Start by remembering that this is a stage. The even years tend to be the hardest ones. 15 is coming. Meanwhile, you want her to take pride in herself. What does she do well ? (obviously not personal care routines) Praise her on the things she does well, especially on the process, not the result. We can't always control the results of our efforts,but we can still take pride in the process that got us there -- how we tackled a problem, how hard we worked on something, etc. Be sure to notice those things in her life, and praise her for them. That way when she puts effort into something and that she would BELEVE you when you praise her, she'll really blossom when you do and feel good about the praise.
So she balks at personal hygeine. My eldest was like that. We had to practically force her into the shower, and make sure she actually washed her hair. (or we sent her back in -- I'm sure there were times she got it thoroughly wet and didn't wash it; except that with the conditioner it would be easier to comb -- who knows?) I, too, worried that she would have no friends, etc., but she got VERY involved in high school activities, and in a sorority in college, and she began to do things in college that you'd have thought we were abusing her for having her do (like going mountain climbing and hiking in the woods) She's now an educator on a tall ship, and she teaches kids about sailing traditional ships, about marine life, and marine ecology. She is amazing with middle school aged kids, because, she admits, "I was a real brat then, and I know what it's like. I can handle them-- I think they're a challenge, and I get to win!" She's funny about it, but she does live in a world with no on board shower !! (we laugh about that ! You get to swim to clean up, or a deck shower in a bathing suit periodically, and then a real shower in port.)
I would try to order my language to you can do this "after you get such-and-such done", or 'when you get it done", and if she really wants to go out with her friends, she'll get the hygeine stuff done. Try not to get emotional about it, but be matter of fact about it. If you don't buy into the emotional stuff, she'll catch onto the rules, and she'll learn she can control whether she gets to do something or not. Get cleaned up, and you can go out. Stay dirty? Well, okay, then you can stay home. She'll figure it out. And one day, she'll surprise you by getting all cleaned up, and THEN asking to go somewhere or have a friend over. :-)
but, do remember, it's not permanent. It's a stage. And hygeine sounds like it is just something to fight over. Sometime later, there will be a different item for controversy, but for now, it's this one. . . .:-) But with this one, try to put in place the kind of behavior on your side of the game that helps you do use the same patterns as the issues become broader as she ages. Be calm, know what you want for a result, and work toward achieving it. Be sure not to remove love as a disciplinary action, and be sure to praise her for the things she does well. As her self esteem grows, over things SHE is proud of, she will begin to take pride in other areas of her life, too. And she will really warm up to having Mom be proud of her - which will help to make her want you to be proud of her future choices in life. :-)