I remember a conversation I had with a parent who was so annoyed with her 13 year old daughter. This teen was giving her mom strict orders on what to wear when she picked her up from soccer practice; "do not under any circumstances wear your matchy, matchy nylon sweatsuit outfit, and make sure you take a shower before you pick me up, do not come straight from the gym, and oh yeah, don't put on your stupid radio station, and don't ask anyone any questions!" As you can imagine, the mom was not a happy camper. Who exactly was doing who a favor here. Than of course there are the orders a parent receives from their teen about the expected behavior if a bunch kids are coming over on a weekend night" Do not come downstairs, do not ask any question, do no exist!!"
First of all do not do not do not take any of this dither personally. Though it feels very personal, it really is that teenage brain talking with a new understanding that other people are thinking things about them now. Not only are they being judged, but everyone connected to them are part of the judging package including even the beloved family dog. Once their most cherished companion, now, smelly, ugly, annoying, etc.
Relax, this new level of hyper self-consciousness is time limited. As they become more confident and comfortable with their new body and new brain, usually juniorish year in high school, they won't be nearly so judgemental. They'll be other things, but not that. This is not a character flaw of your teen, it is completely normal, just unbearable.
Rather than feel like you are being ordered around, and hence a set-up for a power struggle (read argument) "You don't tell me what to do!!" or you say with conviction "That really hurts my feelings" said with profound sadness. You need to have a different strategy. What you need to let you teens know is that they don't get to "tell" you what to do." You might say: " I get right now my style of dress, personality, the way I cook, they way I speak (fill in the blank) all feel embarrassing to you in front of your friends. And I get that causes you some worry. I will do the best I can not to make you feel worried and embarrassed. Letting me know what those things are is helpful, and I will be open to listening and doing what I can. But I won't respond to being ordered about. Just so you know" When your teens start with the ordering, you can always say: " Is there a question there you would like to ask?' This lets them know, that you might choose to accommodate, but you won't be ordered too.
Understanding and not judging this embarrassing stuff gives you some distance so as not to take this too personally. My mother was a constant embarrassment to me as a teen, I bet yours was too.