My daughter of 16 has recently started acting out. She lost her job for being late or missing work.
Was this a reflection of her overall work ethic, or a departure from her typical level of responsibility? Her occupation at this stage of her life is being a student, so I'd be more concerned about how well she performed in that capacity than with a summer job. If there's a systemic issue of her neglecting to manage her time properly and chronically being late, or failing to fulfill her duties, then I'd suggest working with her to develop better habits. That sort of behavior is a form of self-sabotage that can jeopardize what she'll be able to achieve in her life. If she's a strong student, and is otherwise dependable and on track for a promising future, I wouldn't harp on a summer job.
She won't tell me where she is going or isn't where she said she was going. I track her phone and it gets shut off.
Why do you feel the need to know where she is going or to track her movements? Is there a worry that she's endangering herself or doing something illegal? Curiosity about her plans is fine, but I don't think she should feel compelled to always detail them for normal activities. If she's wanting to go away for the weekend, or stay out past 1, or something substantial like that, then of course you'd be entitled to know, but if she's merely going out with her friends during typical hours she probably feels like her discernment should be trusted enough to make simple decisions for herself without running them by you. If she's done something to weaken your trust, then cooperating with her on ways to build it back would probably work better than making her feel defensive and like she has to be sneaky in order to maintain her social life.
When you were a teen the technology to track location via phone wasn't readily available, and you and millions of others made it safely into their adulthood. My parents do have the ability to track my location via my phone, and it's a condition they gave for continuing to pay the bill for it, but they only do so when there's an actual need. I have a life-threatening medical issue, and so when I don't return a text or call within a time frame, they get worried and track my location. They don't do that to my 16-year-old brother who is perfectly healthy, unless it's imperative.
And she is disrespectful to me and her mother. I have grounded her and took stuff away. It gets better for a few days then back to bad. Any advice?
I think respect is often reciprocal, that people are more likely to give respect to those they feel have extended respect to them. Have you asked her if she feels that you respect her, and then genuinely listened to what she said? The disrespect could be a symptom of a problem rather than the problem itself.
If punishments aren't correcting the issues, then perhaps they're not useful. I don't think punishments should be given after age 14 or so, unless there are exceptional circumstances. From that age on you're transitioning towards adulthood, and should be learning more about adult consequences. Her consequence for failing to show up on time for her job was to lose that job and the income it was giving to her. I don't think it would be fair to take away what she already owns, or fail to provide what she needs, but it would be reasonable to not give her money for more trivial things she wants that she could have bought for herself with money she earned.