Obviously the more you challenge her about this the more she will dig her heels in.
Does she even admit to being unhappy Op? Or lonely? Has she told you that her lack of friends is making her upset?
It’s a shame she won’t see a counsellor as just seeing someone outside the family who can say “chill, you are normal, loads of teens go through this and don’t find their tribe until later in life” can be so helpful.
Maybe just gather together a bundle of information for her from Young Minds, the Autism Society, with books about the teenage brain, depression in adolescence, and books about adolescence generally, info on gp and local counselling services and a journal and a nice pen, and present it to her with a note and flowers saying that you think she clever, funny and beautiful and you know times seem hard atm but she will find her way and even though things are difficult, you believe in her etc and in five years time her life will look very different.
There are some highly intelligent women on You Tube who discovered they were autistic later in life. One of them is called Yo Samdy Sam and my dd found her very helpful.
And buy some books about female teenagers by Lisa Damour for yourself op and check out her website. I found Untangled particularly helpful.
If your dd is refusing therapy then I don’t think there is a lot more you can do at the moment except step back a little, continue to make it clear that you love her and she can come to you about anything but you don’t want to argue any more.
Also maybe talk to her gently and suggest that she is in charge of her own life now and she has more choices than she thinks eg about whether she wants to apply herself to college or not (but say this in a very sympathetic way) that you are really interested in the choices she makes and you are happy to help her with anything she is finding difficult that is stopping her from getting up early or studying. But ultimately it’s down to her.
This subtlety shifts the responsibility back on to her. You don’t need to be stricter but you let her suffer the natural consequences when she is late or doesn’t study hard enough.
Maybe talk to her a bit about how she sees her future. Grab some info on university courses or apprenticeships she is interested in. Maybe give her a glimpse or two of the adult world - can you take her to your work - and show her a couple of nice aspects of adulthood and demonstrate why growing up isn’t a wholly repulsive prospect! Sometimes our dc only see stress and worry at home and not enough fun or reasons to become an adult. Not saying this applies to you op but be aware of how you and your dh handle stress. Not always easy when ironically your dd is adding to it!
Being stricter only causes more frustration at this already frustrating period in- between stage when she desperately wants freedom but isn’t yet mature enough to live independently, but at the same time op, hold your boundaries. Very quietly and calmly. Never get involved in an argument. Step away when she starts being horrible or raising her voice. Leave the house if you have to. Tell her you will be happy to speak when she is calm.
Ignore anything that is bluster, frustration, juvenile rudeness, or point scoring, just don’t get involved, choose your battles, and reserve your responses for outright hatefulness! Just try and be calm and consistent and sympathise but don’t tolerate outright rudeness because some frustrated neurodiverse teens seek a dopamine hit by baiting their parents. Don’t let her do that.
Also try and engage with her over one thing that she is interested in and that is external to home and college, whether it’s a sport, a hobby, films, junk food, a book you are both reading, volunteering at an animal shelter together, wildlife, photography, crafts, clothes or make up shopping - depends on her interests - just do one thing together that’s fun and do it every week regardless of how horrible she is being.
Don’t turn it in to a battle but make it clear that you will only engage when she is speaking to you respectfully and try not to get beaten down by it. Getting ground down by worry about her won’t help anyone.
In five years time, things will hopefully be very different. All teens develop at different rates and progress is rarely linear but it will come in fits and stops and starts. It just takes time. And if she does have ASD remember that autism in essence is a developmental issue ultimately, putting it very crudely.
Another thing that can be helpful at this age is animals. Do you have any pets? Would you buy her a dog, cat, or a pair of guinea pigs if she is interested? Pets, chosen wisely, can dilute any tensions at home and be a good positive talking point when there isn’t much else to be positive about,
Focus on your own life a bit more op and model having fun and going out and enjoying friends. And invite your friends home a little. Your dd needs you to be firm, reasonably positive and stable, so you and your dh should grab on to any support you need to get yourselves back in to a happier place. And that includes counselling for yourself if you are finding this situation is seriously affecting your mh. Don’t allow her bad moods to dominate the home. Keep the positivity going if you can. Not in a false way but choose humour where you can.
Hang in there op 💐. Although you feel helpless, remember that by just being there and continuing to love her, despite her being unkind and horrible, that is ultimately helping her. I don’t mean indulging the poor behaviour but loving her despite of it, loving her as a person but not her current actions , gives her the message that despite how crap and lonely she feels inside, she is worthy of love and that message will eventually get through! Good luck!