Leaving a 16 year old "on his own for a few days at a time" is potentially illegal. See these sources:

At What Age Can My Child Be Left Home Alone? - Calgary's Child Magazine

When Can You Leave a Child Home Alone? - FindLaw

I believe most responsible parents would consider it highly inappropriate, to say the least. Doing so has been known to lead to tragedy. Here is a link with guidelines. (below) What is appropriate depends on the child's maturity. To say, "My kid is a problem, so I'm leaving him alone to let him grow up," is a line of reasoning that would probably strike most family court judges as deplorable. It strikes me, in this case, as highly self-serving, especially when the mother wants to go on a date lasting several days. A man who gets a woman's company on this basis has zero reason to see such a woman as worthy of respect.

Guidelines for Leaving Kids Home Alone with Printable

The child's father would have every right (even a duty) to report this to family court.

How does leaving a child alone teach him that money doesn't grow on trees? Threatening to abandon a child for bad behavior is child abuse. Disparaissant, you are profoundly confused about your rights and duties. You should ask family court to provide you with counseling. If I were your next-door neighbor, I would report you to Child Protection Services.

Every parent says their children are their priority. That's just talking the talk. You have to walk your talk.

You just don't leave a 16 year old boy with a history of behavior problems home alone for days. You just don't do that. You just don't.