Teenagers are hard. They can often be unmotivated, self-centered, messy, and tired. As a nurse, I know that some of that is because of their age. Did you know that the average teen needs 8-10 hours of sleep each night? And yet they tend to be completely resistant to sleep.
There's a problem in those two facts!
But as much trouble as they are, having them at home can be a huge help. At home they can get the sleep they need while at the same time attend school regularly. If they were in public school, what time would they need to get up to meet the school bus? And what time would they finally finish their homework? So yes, homeschooling can help even with the most basic needs of teenagers.
Being unmotivated is a major issue that ALL parents of teenagers face from time to time. If your child was in school, their lack of motivation and self-centeredness might not be any different that it is now. The major difference would be that while homeschooling, they have YOU. They have a parent, a loving adult, to shape and mold their behavior in the midst of their teenage issues. They get feedback from a parent who encourages them to not be self-centered, who expresses concern about motivation. What you don't want is for the child to be surrounded by other children who feel the same way, and reinforce bad habits and behavior. Imagine how it would be if they had no one to lovingly encourage them and become mature.
I guess I have focused too much on the differences between public and homeschool in the contrasts here. I apologize, because I really do try to avoid comparisons between school situations. But teenagers are hard, and it might not be any better under any other circumstances. In fact, homeschooling may be the best possible situation to handle these issues.
Best of luck with your teens! Be strong, be patient. Remember your five-year plan; strive to be a loving family in the end, when they are adults!
Just remember in the midst of conflict that "this too shall pass." Oftentime something miraculous happens when they turn 20. Hang on! You will make it!