Hello iveygirl and welcome.
Please know that you had nothing to do with his desire to return with his father.
At this point in his life,he's conflicted and until he initiates resolve by truly realizing that he has a problem and is willing to do something constructive about it,chances are,it will remain this way.
I'm not going to say that I know what you're going through but I can only imagine how my parents viewed me around the holidays.
Unconditional love on one hand with tough love on the other.
I wonder if he left because he didn't want to cause any embarrassment for you or his brothers during the holiday season.
A wounded bird will only stay in your house,if it feels comfortable.If it senses the least bit of objection to it being there or feels out of its' element,it will try earnestly to leave.
Please know that I feel for you;truly.
Unfortunately the path that he chose to travel must be done alone.Hopefully along the route,he will become enlightened enough to see the vicious cycle,which effects more than just him.
I pray that he eventually sees this.
Respectfully stated during the holiday season