When I was in high school I came up with my own training plan. I never outright told my coach that I was doing my own thing (although he figured it out when I'd run past his house every morning for doubles). By the time we had that talk I had already proven myself with results. If I was slower he might have put a stop to it.
I think the most important thing is that you don't make too many changes during your actual practice. Going for an extra 10 minutes on a run is one thing, but don't skip or sandbag workouts. Even if a workout isn't ideal, it will still help your fitness. In my experience, even the "bad" programs write decent track workouts. Even if the workout sounds stupid, it can usually be saved by adjusting pace/rest/reps.
What I think you should do:
1. Work on the little things at practice. Drills, warmup, core, etc. Do them at home if you have to.
2. When you're at your HS practice, listen to your coaches. Only go against them if it's a minor change or if it will make a big difference in the quality of your training.
3. Do whatever you want with your private coach, as long as you are recovered and ready for team practice.
4. Once you have some results to back yourself up with, consider telling your coaches.
5. Once you become the local superstar, you can brag. Remember that your race results justify your ego, not how much time you spend with a private coach. I've seen kids get carried away with that, so I hope you don't do that too.
Now I strongly recommend ditching the private coach and instead getting free advice here. But that's neither here nor there. All I can say is good luck. The hard work will pay off.