Well. Josh, technically, I think you are plenty old enough at 16. Some kids are soldiers and fighting wars at 16. Some kids are parents at 16. The key is that you need to prove to mum that you can be responsible. If I were you I would write a checklist of all the things that you know you need to do when you are home alone. Write things like, lock the doors and double check them, clean the house, reheat or cook simple meals and at what time you plan to eat them, even write things like taking a shower and when you plan to go to bed and wake up. Also tell her that you will call her twice a day, in the morning and at bedtime.
What she is concerned about is your ability to be responsible. If you are proactive and show her that you intend to be and are capable of sticking to a written contract that you and she come up with together and agree on, I think she might let you try it. And if you do stick to it and succeed, this will be a huge milestone for both of you. She will see that her baby is growing up and can be trusted and you gaining her trust will be huge and this could be a great step towards your eventual independence.
But if she lets you do it, you must stick to the contract and be absolutely above and beyond in your responsibility and integrity. If you do something stupid it will set you back years.
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"I'm bad and that's good. I'll never be good and that's not bad. There's no one I'd rather be than me."
Wreck It Ralph